I have an iOS app that I've made using a free provisioning profile, in order to give the app to people though, I have to plug their phone in to my computer and install it with Xcode. I was wondering if there was a way to let people download the app from my server without paying for a license.
No, the only way to do this (install on another person's device without having their device set up explicitly in a developer profile) is to use an enterprise development account. This type of account (which costs even more than the $99 standard developer account) allows you to create an enterprise distribution profile that allows for distribution on devices that have not be set up in advance. However, the enterprise account is even more money and you must have an EIN (like a SSN for companies).
So to answer your question, no there is no way to do this.