No, you do not complete a Schedule F if you are not the owner of the farm.
You are an independent contractor and need to report your income and expenses on Schedule C.
See this TurboTax support FAQ for schedule C - https://ttlc.intuit.com/turbotax-support/en-us/help-article/import-export-data-files/enter-schedule-...
If you are using the TurboTax online web-based editions you will need to upgrade to the Premium edition for Schedule C
