Will my apartment approval be affected if I file for chapter 13?

It sort of depends on whether the landlord checks your credit report again, and if so, what kinds of credit reporting they use. Landlords typically look for credit problems such as utility shut offs and evictions, not bankruptcy.

How would your new landlord even know about your chapter 13 filing? It's not stamped on your drivers license, after all. Generally speaking your filing is not likely to make any difference with a lease that is already in existence. But, there is no accounting for watch a landlord might find out, and how she will react to it. I don't think there's any specific law governing this situation: it's something that people work out. If your credit was good enough for the landlord a week or a month ago, it's probably going to be enough after you file your chapter 13 petition.

I would recommend waiting to file until after you signed the lease.