I'm planning on building and deploying a static site on github. If i was to do that is it still possible to have a contact form?
It seems that's the only set of dynamic functionality that's going to exist on my particular website.
Would i have to create a service somewhere else to create the contact form?
Yes, you'll need to use an external service. A great external service for this that requires no signup and is free for up to 1000 submissions per month is Formspree.
Other options: Simple Form (Free), FormKeep ($19/mo.), & Wufoo (Free & Paid Options)