The 25-year-old, who has never started a regular season game, has previously played as a right guard.
Brewer, who is preparing for his third season with the Giants, told the team's website: "I haven't been on the left side since last pre-season when they had me do some left tackle.
"I'm very excited to be playing left guard. Honestly, just the chance to start is big for me and whether or not I'm on the left side or right side, as long as I'm on the field. My main objective is to be on the field.
"Nothing's set in stone, they're just kind of shuffling things around, seeing which best five is going to give our team the best chance up front and I just look at it as a shot to prove that I'm the next guy up."
The Giants face the New England Patriots tomorrow night.