Yes. Almost all major credit issuers allow co-signing, but there may be some restrictions. If your father has a credit card with one of these issuers, he should contact them for details.
Co-singing is not the best way to build your own credit history. As an alternative you may get your own credit card instead of having your father co-sign. You may apply for a secured credit card. You will need to put down a security deposit for the credit limit. Your credit performance will be reported to the major credit bureaus and you will be able to build a good credit history.
Disclaimer: This editorial content is not provided or commissioned by the credit card issuer(s). Opinions expressed here are the author's alone, not those of the credit card issuer(s), and have not been reviewed, approved or otherwise endorsed by the credit card issuer(s). Reasonable efforts are made to present accurate information, however all information is presented without warranty. Consult a card's issuing bank for the terms & conditions.
All rates and fees, and other terms and conditions of the products mentioned in this article/post are actual as of the last update date but are subject to change. See the current products' Terms & Conditions on the issuing banks' websites.