How to Check Your MMR in Smite
To check your MMR in-game, all you have to do is go into your profile settings and it should show you right away.
If you don't know how to get into your profile settings, all you have to do is click on your profile icon in the top right corner and it should take you there. It's important to note that Smite tracks your ranks differently for the different game modes. A Diamond player in Conquest will not be a Diamond player in Joust and vice-versa.
This is a no-brainer, but your matchmaking rating is based on your activity. I haven't been playing too much on my alt account, so hence why it's unranked. 1500 is the average MMR in Smite for unranked players across the board. If you're a Grandmaster, that value can jump well into the 3000s. Which tends to be the highest MMR in Smite achievable by players.
How to Check Your MMR Online
There's also an alternate method to checking your MMR, however, it's not always the most accurate.
There are a couple of sites online that allow you to look up a certain player. The most prominent example being SmiteGuru. Whenever you look up a player on SmiteGuru you get a detailed report on their game history. From the game mode that they most often play, to their achievements in previous seasons, to their best role in Smite, aka, the Gods they play most. It even shows their win rate.
The system tracks everything. If you want a better-looking report, have higher quality matches. Simple as. Just keep in mind that online trackers aren't always the most up-to-date. Take for example the report of my alt account. The last update it received was from a year ago. So it isn't quite "the most accurate", but hey, what can you do?