As many of you are aware, Discord allows you to create invitations to the servers you create. However unless you have a partnered server, you have no control over the randomly generated string. It also looks like that Discord has no plans to implement this for non-partnered servers, per a post by Dabbit Prime (Discord Admin) on June 15, 2017:

This feature is only for partnered servers and will remain that way.

There's a few ways to get around this yourself. You can use Discord.me, or if you have your own domain you can set up a DNS record, or again if you have your own domain as well as web hosting then you can set up a redirect via an HTML file or .htaccess file. For example, I use crunchprank.net/discord and to accomplish this, I just have the following line added to an .htaccess file in the root of my public HTML directory:

Redirect 301 /discord https://discord.gg/nhZvTcm  

But if you can't be bothered with any of the above, I launched a site that serves as a simple custom URL redirect for your Discord server: dscrd.me. Originally intended and used for a few of my friends, I decided to just offer the service to everyone. However, unlike Discord.me, there is no user interface. At one point I might implement this, but in doing so it would open up the possibility for users to reserve custom URLs containing names/brands that they're not affiliated with, which is the one thing I dislike about Discord.me. And I personally don't feel like having to spend time moderating that type of stuff. So for now if you're interested in getting your own URL, you can submit a request via the form here. The domain is dscrd.me so your URL would be similar to dscrd.me/crunchprank. Also, the domain is protected by CloudFlare with encrypted traffic over SSL/HTTPS via a LetsEncrypt certificate installed on the server in case you care about that kind of thing.

So in short, the project is dscrd.me and provides free, custom URLs to forward users to your Discord server. Submit a request via the form to get one set up.