You can use open chords for the Chorus but he used barre chords for the verses. 
The barre chords are:  Dm (5th fret Am shape), Fm (10th fret Am shape), A (5th fret E shape) 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

     Dm                  Fm 
Said prepare me for, for long battle 
       A 
I am a witness hope is steel bullets  
           A 
I drop the hatchet you won't forget this 

     Dm                  Fm 
Said prepare me for, for long battle 
       A 
I am a witness hope is steel bullets  
           A 
I drop the hatchet you won't forget this 
      Dm 
Said, mine eyes have seen nothing but trouble 
    Fm 
You must make peace with them gods and the devils 
     A 
I can be rude boy, I am not subtle 
     A 
I tend to sneak and burst all them bubbles 
Dm 
We are the ones we been waiting to rumble 
Fm 
I torch my enemies out with a candle 
     A 
Music is the weapon make empires crumble 
     A 
We bring them bankers and wealthy to tremble 

Dm              Fm 
What we know is what we're owed 
             A 
Can't be too careful, shoot flaming arrows 
             A 
Hitting them wicked, burning them bridges 
      Dm              Fm 
Said, what we know is what we owe 
             A 
Can't be too careful, shoot flaming arrows 
             A 
Hitting them wicked, burning them bridges 

Dm 
I rep the misfits, not society 
Fm 
We struggle with housing, drugs and sobriety 
      A 
We're not from here but born here respectively 
      A 
Immigrated cuz America raped my country 

   Dm 
My bridge 'aint built with no white man money 
       Fm 
I'm on Indian time you know you cannot rush me 
         A 
I can be vicious malicious and ugly 
            A 
A danger to darkness to better run quickly 

Dm              Fm 
What we know is what we're owed 
             A 
Can't be too careful, shoot flaming arrows 
             A 
Hitting them wicked, burning them bridges 
      Dm              Fm 
Said, what we know is what we owe 
             A 
Can't be too careful, shoot flaming arrows 
             A 
Hitting them wicked, burning them bridges 

      F                    C 
Said, I've come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

      Dm 
Said, life was pretty crazy I was 9 months old 
      Fm 
Yeah, momma gave me up at 14 years old 
        A 
Said, I don't give a shit grandmother she was so bold 
            A 
Some of the rapist mommas body got sold 

       Dm 
Not to say poppa didn't have a good soul 
       Fm 
Cuz he did give me the anger I was born so cold 
             A 
Raised white Christian in a white neighborhood 
             A 
There was no bridges for me and my indigenous blood 

  Dm 
I said I'm confused, identity crisis 
Fm 
Indigenous mastery is so timeless 
        A 
Now I'm building bridges so that it will all make sense 
        A 
Why I'm here with the music so passionate 

Dm 
Got to ride hard or die trying 
      Fm 
Said, I am a raincloud storm white lighting 
          A 
I am relentless stop at nothing 
          A 
I'm el coyote bridges building 

Dm 
Said, I rock the one feather on me next head 
          Fm 
Must stay humble, never be like chief headdress 
         A 
Hang the flag upside down I'm in distress 
           A 
Never take no title out of deepest respect 

Dm 
Welcome to aquarius son you’re a legend 
Fm 
Guardian of the gate it's gate number 7 
            A 
I tame that beast and I ride the dragon 
            A 
I reincarnate as a wild stallion 

Dm              Fm 
What we know is what we're owed 
             A 
Can't be too careful, shoot flaming arrows 
             A 
Hitting them wicked, burning them bridges 
      Dm              Fm 
Said, what we know is what we owe 
             A 
Can't be too careful, shoot flaming arrows 
             A 
Hitting them wicked, burning them bridges 

      F                    C 
Said, I've come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

F                      C 
I have come to build a bridge 
              Dm 
So come let's build 
Dm 
Build build build 

Dm                        Fm 
Said, my people my earth, my country, my heart 
           A 
In service for ever, a mission to better 
   Dm                  Fm 
My passion my fist, my heart open it 
           A 
Reclaim recover, protect clean water 

      Fm                   C 
Said, I've come to live in peace 
              Dm 
So come let's live 
Dm 
Live live live 

      Fm                   C 
Said, I've come to live in peace 
              Dm 
So come let's live 
Dm 
Live live live 

      Fm                   C 
Said, I've come to live in peace 
              Dm 
So come let's live 
Dm 
Live live live 

      Fm                   C 
Said, I've come to live in peace 
              Dm 
So come let's live 
Dm 
Live live live