Wow. Just three? Okay, I would start with one of my personal favorites, Brian Turner. He's very new to the field, but his book Here, Bullet is a brutal discussion of the war and the social issues revolving around that war from the hardening of hatred to the psychological damage done.
Number two would be Nikki Giovanni, but since someone else has already discussed her genius, I'll go with Mark Turcotte who really has an incredible way of describing modern Native Americans caught between their culture and contemporary America. Beautiful imagery and really shocking contrasts make me adore his poems.
Number three (again just a personal choice) would be Sylvia Plath. I really do like her stark images and the surprising way she talks about every issue. "Morning Song" is such a little gem that I just sort of stare at it in wonder. Her issues are focused far more on the family and are more personal than my other two choices, but those would be my picks.
There are many more than three contemporary poets who write about social issues. Since you've asked for three, I'll limit my answer to that number and maybe somebody else will give you more.
Nikki Giovanni is one contemporary poet and is also a professor at Virginia Tech, where what has been described as the worst mass murder in American history occurred. She has written many poems, but one of the most poignant is the one she wrote for the memorial service for the victims of the VT shooting. Search for her here at eNotes or click on the link below for that and more poems.
Another contemporary poet is Lucille Clifton. Her poems speak about being a woman, particularly an African American woman. Her graphic imagery make her poems powerful. One of my favorites is "Homage to My Hips." I don't have enough space to add it here, but look for Clifton here at eNotes and at the link below.
A third poet you might want to look at is Gary Soto. His writing reflects his Mexican-American heritage. In "Mission Tire Factory, 1969," he writes about four Chicano men working in a factory. You can find that poem at poethunter.com.
There are many, many more poets who write about social issues. Good hunting!