At a news conference in Des Moines on Sunday, Robinson apologized to friends, family and former teammates for breaking team rules and Iowa law by possessing marijuana.
"I know I have disappointed you and let you down," Robinson said. "For that, I am sorry."
The 21-year-old Robinson was charged with possession of marijuana Dec. 27 in his hometown of Des Moines. The Iowa State Patrol said Robinson was a passenger in a vehicle pulled over for not having a front license plate. A trooper detected a marijuana odor from the vehicle, then found marijuana after a search.
Iowa coach Kirk Ferentz suspended Robinson for the Dec. 28 Insight Bowl, which Iowa won 27-24 over Missouri. Ferentz kicked Robinson off the team Jan. 3. Robinson said Sunday the dismissal was for academic problems.
Robinson pleaded guilty to the possession charge and was fined $315 and given a year of probation.
On Sunday, Robinson said he had resisted offers to play at other colleges because he intended to prove himself worthy this semester of returning to the Iowa backfield.
"I've always wanted to be a Hawkeye," Robinson said. "I have no wishes or desires to leave the Hawkeye team."
Robinson said he intended to undergo drug counseling in Iowa City and work on raising his grades, too.
He has not talked to Ferentz about those plans, Robinson said.
Robinson rushed for a team-high 941 yards and 10 touchdowns in 2010 as the Hawkeyes' featured back.
Spokesman Steve Roe said Iowa officials would have no statement Monday.
Robinson said his hopes of returning to the team were raised when he read that after being on suspension for eight months, Iowa wrestler Montell Marion had been reinstated to practice. Marion was suspended after an arrest for drunken driving.
Robinson said he never failed a drug test while at Iowa but acknowledged using marijuana several times. His drug transgressions were limited to pot, he said.
His mother, Sally Robinson, was with her son to face reporters Sunday, and she suggested that she blamed his drug abuse in part on two concussions he suffered late in the season.
"He had a meltdown the first part of December," his mother said.