Aiken, 27, is expected to add depth to the Colts' receiving corps.
Aiken played for the Baltimore Ravens last season, and had 29 catches for 328 yards and one touchdown. He had a better season in 2015, when he posted team highs in receptions (75), receiving yards (944) and receiving touchdowns (five).
In 51 career games, including 20 starts, he has caught 128 passes for 1,539 yards and nine touchdowns.
"Kamar is a tough competitor and has shown he can be a consistent wide receiver in this league," said Colts general manager Chris Ballard. "He adds a nice complement to our wide receiver group and we look forward to watching him compete."