Since the other two major credit bureaus, Equifax and TransUnion, don't currently receive rental payment history, your rental history won't affect your score with those bureaus.
You won't be able to see how rental history affects your FICO score since Experian doesn't allow FICO to sell scores based on Experian credit report data. However, lenders may still use this score so it's important to keep paying your rent on time. If you're late on your rent payments or you get evicted and the landlord reports this delinquency to any of the three credit bureaus, including Equifax and TransUnion, that will hurt your credit score.
If you want to see how your credit score is doing after rental history gets added to your report, you'd have to check your Vantage Score, which is available through Experian.com