If I apply for credit, will my credit score drop?

According to FICO, if it does, it probably won’t drop much. 

When you apply for credit, the lender accesses your credit report, creating what is called an inquiry. Multiple inquiries in a short period of time typically are treated as a single inquiry and will have little impact on your credit score. For example, the score counts multiple auto or mortgage inquiries that fall in a typical shopping period as just one inquiry; older versions of the scoring formula count the shopping period as any 14-day span, and newer versions count the shopping period as any 45-day span. Each lender chooses the version of the FICO scoring formula it wants the credit reporting agency to use to calculate your credit score.