The 24-year-old, who worked with Dons boss Neal Ardley at Cardiff, has been without a club following his release by Aldershot in the summer.
Morris spent three years with the Shots before a long-term knee injury ended his stay there.
Ardley told the club's official website: "I coached Aaron when I was at Cardiff, where he came through the ranks.
"When he first joined, he was a central midfielder, but I noticed that no-one could beat him in one-on-one situations so I played him at full-back.
"He was outstanding and managed to make the first-team squad at Cardiff. He played in central midfield for Aldershot last season and I know that they were very disappointed to lose him when they were fighting relegation.
"Aaron can play in a number of positions, but he can be a very good centre-back in my eyes. When he suffered an ACL injury I sent him my best wishes and said there could be something here for him if he got strong again.
"I would have signed Aaron in the summer if he was not injured. Aaron is a very powerful athlete and once he gets himself fully match sharp then the fans will see what a good player he is."