If I work for my rent and no cash is exchanged how do I list this on my taxes ?

You have "barter" income ... rent for work.  

https://www.irs.gov/taxtopics/tc420#:~:text=Reporting%20Bartering%20Income,from%20Business%20(Sole%20Proprietorship).

Bartering is an exchange of property or services. You must include in your income, at the time received, the fair market value of property or services you receive in bartering. 

Generally, you report this income as self-employment income on Schedule C Form 1040. 

In TurboTax Online, click on Wages & Income and Self-employment income and expenses down the left side of the screen.

If you exchange services with another person and you both have agreed ahead of time on the value of the services, that value will be accepted as fair market value unless the value can be shown to be otherwise.

IRS Publication 525 Taxable and Nontaxable Income, page 20 

However, you do not include in your income the value of meals and lodging provided to you and your family by your employer at no charge if the following conditions are met.

The meals are: 

• a. Furnished on the business premises of your employer, and 
• b. Furnished for the convenience of your employer. 

The lodging is: 

• Furnished on the business premises of your employer, 
• Furnished for the convenience of your employer, and 
• A condition of your employment. (You must accept it in order to be able to properly perform your duties.)

IRS Publication 525 Taxable and Nontaxable Income, page 8

@ambercrocker1976