Yes, you can absolutely use Patreon’s logo to promote your Patreon!
Here is a bit more language about how you can/cannot use it, taken from our Terms of Use:
Creators can use our copyrights or trademarks to promote their Patreon pages, but can’t use them for anything else without our permission.
Our creations are protected by copyright, trademark, patent and trade secret laws. Some examples of our creations are the text on the www.patreon.com site, the text on Patreon’s other websites, our iOS and Android apps, our APIs, our embeds, our logo and our codebase. We grant creators a licence to use our logo and other copyrights or trademarks to promote their Patreon pages.
You can learn more about the correct use of our logo in our Brand Guidelines.
You may not otherwise use, reproduce, distribute, perform, publicly display or prepare derivative works of our creations unless we give you permission in writing.
Please ask if you have any questions.