Can sperm cause a girls vagina to burn?

Maybe you have an infection or STD the long and short of it is... It shouldn't.

One possibility is small tears inside the woman react to the different PH level of the sperm.

This is especially possible, if the man is well endowed, the female smaller, and not enough foreplay/lubricant is used.

Another possibility is... maybe it's not the sperm itself that's "burning" but the continued thrusting after ejaculation has begun. Pre-ejaculate can begin effecting the lubrication of the vagina long before "actual" ejaculation(this is the very basis for some of the tantric sex techniques). When this happens, the natural lubricant can be , litterally, neutralized.

A final possibility is , you may actually be ALLERGIC! It's very rare, but does happen, and the allergy can manifest itself with a large number of symptoms, possibly even the burning sensation when in contact.

Either way, you should SERIOUSLY contact your gyn, and get a check-up. And in the meantime, practice safer sex. Use a condom. If burning continues when using a condom... either the condom broke, or you've got yet another symptom to talk to your doctor about.