The Texas congressman won Saturday's poll with 52 percent of the vote. Paul won in both online and total votes.
Former Massachusetts Gov. Mitt Romney carried Illinois' in-person voting with 35 percent.
The Illinois straw poll -- at more than 3,600 votes -- surpassed such large states as Ohio, Florida and California that held straw polls earlier this year.
Online voting started Oct. 29 and paper balloting went on throughout the day Saturday at about two dozen Illinois sites.
Any Illinois voter could cast a ballot in the GOP straw poll with a $5 contribution to the state party. The Illinois primary is March 20.