Yes, you may port your US toll-free and local numbers number over to Twilio, just like any other telephone company. Currently, Twilio is not able to port numbers based in Hawaii, Alaska, and areas in the US where Twilio does not provide service, as well as Canada, and other countries outside the US. For more details on porting numbers to Twilio, please visit https://www.twilio.com/help/faq/porting
Alternatively, you can verify a phone number with Twilio so it can be displayed in the Caller ID while Twilio uses another number. This will allow you to keep everything the same with your existing phone setup and extend it with Twilio.