Yes, Iowa does offer a Tax credit for house rent paid, if you qualify.
Iowa Disabled and Senior Citizens Property Tax Credit/Rent Reimbursement
Description: Incorporated into the Homestead Tax Law to provide property tax or rent relief to elderly homeowners and homeowners with disabilities.
Eligibility: Must be 65 or older or totally disabled, and meet annual household low income requirements.
Filing Requirements: A property owner must file a claim with the county treasurer by June 1 preceding the fiscal year in which the property taxes are due. Renters must file with the Department of Revenue by June 1 to claim reimbursement for rent paid in the prior calendar year. The director or county treasurer may grant extensions of time to file.
Forms: Property Tax Credit Form 54-001
Rent Reimbursement Form 54-130