Yes, but they HAVE to let you do it (take your phone number with you, whether they want to or not. It's the law).Portability: Keeping Your Phone Number When Changing Service Providers
Under the Federal Communications Commission’s (FCC’s) “local number portability” (LNP) rules, so long as you remain in the same geographic area, you can switch telephone service providers, including interconnected Voice over Internet Protocol (VoIP) providers, and keep your existing phone number. If you are moving from one geographic area to another, however, you may not be able to take your number with you. Therefore, subscribers remaining in the same geographic area can switch from a wireless, wireline, or VoIP provider to any other wireless, wireline or VoIP provider and still keep their existing phone numbers.
As noted in the quote above, there are limitations though.
And there may be fees involved, but they have to do it.