The "My, Myself & I" rapper adopted the pittie, named Phoenix, and we're told the pup had been abused by a homeless man before landing in a Los Angeles animal rescue.

G-Eazy rescued her from The Labelle Foundation, which tells TMZ ... Phoenix had been posted on their site for 2 months, but hadn't gotten many inquiries.

We're told G-Eazy saw the adoption post and reached out to the owners of The Labelle Foundation through a mutual friend, and he came by Monday to pick her up.

G-Eazy and Phoenix wasted no time getting to know each other -- after he picked her up, they hopped in his classic car for a drive through the Hollywood Hills, stopping for a bite at the famous Beachwood Market near the Hollywood sign.

It's a big step up for Phoenix ... we're told a Good Samaritan saved her from being kicked and abused by the homeless man. She's since been boarded, trained and is obviously a very good girl.