A short sale doesn't necessarily affect a person's ability to rent a house. A short sale will have a lowering effect on a person's credit score, and a landlord may take the renter's score into consideration when deciding whether or not to rent the house out. Landlords may be wary of someone who wasn't able to pay their mortgage.
Selling a house for less that it's worth leaves you with an unsecured and non-performing loan with a lender. This could affect your credit score and your rental options. Check your current score. If it's above 700, you should be OK. If not, attempt to rent a house directly from the renter who will bypass a credit check.
A short sale will ding your credit, but it will not prevent you from renting - especially if you find a private rental (instead of a rental property owned by a company) or provide a large rental deposit. You could get a better deal renting from someone who has had trouble selling their own house.
Some landlords run a credit report in the process of evaluationg a renter. A short sale may impact your chances of renting a property depending on the landlords criteria. Being honest with your potential landlord on what is in your credit report is the best way to overcome any negative items in your credit report.