Does limit warranty cover cracked screens?

Your best bet is to take it to an apple store. If you bought the AppleCare+ they'll charge you $50 and give you a whole new phone. If you didn't, they'll either sell it to you within 30 days or I've even seen them cover the replacement costs for a first time accident like that. Definitely cheaper than voiding the warranty by taking the phone elsewhere.

https://www.apple.com/retail/geniusbar/

No, iPhone warranty does not cover cracked screens unless the crack is absolutely due to a manufacturing defect, which is highly unlikely.