Police said they determined Eric Sterson's whereabouts by tracking his cellphone's signals and took him into custody at an Ames grocery store Thursday, WQAD-TV of Moline, Ill., reported.
Rock Falls police said the girl, Joy Haahr, and Sterson had a romantic relationship and allegedly were traveling in a stolen car.
"There is a love interest based on the messages we've read, and being the age of 13, she's very impressionable," said Rock Falls Police Chief Mike Kuepler, referring to text messages the two sent one another.
Haahr's mother, Mary, told WQAD she suspects Sterson began dating her in an attempt to get close to her teenage daughter.
"I should have never let him near me like this, or her," the elder Haahr said.
Police said Sterson, who also goes by the name Eric Smith, has initially been charged with a parole violation and stealing a car.