Can my stepfather adopt me as an adult?

What is the name of your state? GA
I am a 30 year old married adult and I was wondering if my stepfather could adopt me.
My parents divorced when I was 8, saw my father on weekends and holidays for a couple of years. My mother remarried 5 years later, and we (mother, stepfather, younger brother) moved an hour away when I was 15.
My father still lives in the city where he was born and where we lived most of our lives. However, he is an alcoholic, unemployed, and homeless. I literally passed him on the street back in March and he did not recognize me.
Meanwhile, my stepfather financially took care of my mom, brother and me, and has been there emotionally through our growing up. When my son had pediatric surgery, it was my stepfather who drove up to Atlanta to be with the family. And my stepfather is the only grandfather my toddler son knows.
My mother and stepfather talked years ago about him adopting me and my brother, but they decided against it since at that time we still had a relationship with our father.
What would I need to do for an adoption to take place? Would my father need to sign something? What about his state of mind (years of alcoholism)?
I still love my father, and I wish things were different, but I'm really not sure I want to carry the name of a man who hasn't been part of my life for years, and I'd like to honor the man who has been.
And if adoption can be done, how will it affect my marriage license to my husband and my son's birth certificate?
Thanks for your help!

What a wonderful thing to do! I'm sure it can be done. I'm pretty new at this stuff, so I can only suggest the courthouse. They should be able to tell you more info. As you are an adult, I doubt bio-dad would have to sign anything. I mean, he's not giving up parental rights-he doesn't have them.

I'm so happy for you having a true dad! My g-pa is a step, but no one can tell. He has one bio-son and came into eight stepkids and nearly 40 grandkids, and treats each of us like we are his own blood!