Can you finance a house and rent it out?

Generally, yes. This is called a “ non owner occupied” transaction. The lender may potentially have different requirements, including reserve funds, proof of property income (lease, rent roll, etc), slightly higher rates (to account for the difference in risk), sufficient down payment to avoid any sort of mortgage insurance. Contact a local lender to assess your “non owner occupied” purchase options, explaining your intent to rent out the home. DO NOT represent that you will be living in the home if you do not plan to do so for at least a year. This is considered mortgage fraud, and you can be held personally liable for having committed it.