The warrant was signed Tuesday by Flint (Mich.) District Judge Linda V. Parker after authorities said Rison violated his federal probation.
The former Michigan State star pleaded guilty in Arizona in 2012 to two counts of failure to pay child support. He was ordered to pay approximately $323,000.
Authorities claim the 49-year-old Rison has been delinquent in his payments and has paid less than $35,000.
"I'm just tired. Here I am, being looked at like a hardcore criminal. ... I'm trying to do the right thing," Rison told the newspaper. "My mistake was made years ago, and I'm still under this microscope. It's very frustrating."
The warrant also discloses that Rison tested positive for marijuana last month. His probation terms prohibit him from using marijuana.
Rison was a five-time Pro Bowl wide receiver during a 12-year career spent with seven NFL teams. His best seasons were with the Atlanta Falcons from 1990-94 as he topped 80 receptions each season while compiling four 1,000-yard campaigns.
Rison finished his career with 743 receptions for 10,205 yards and 84 touchdowns.