ARAM does have its own ladder, all game modes have an individual MMR in League of Legends.
Your personal MMR is 887, OP, the bottom 8% of players - or in other words 92% of players are better than you are.
https://na.whatismymmr.com/plasma%20servant
ARAM is a heavy teamfight-oriented map, and positional errors are quickly brought out. With that being said, it's also RANDOM. Sure, there's accounts that are specifically brought up for the purposes of team-stacking (i.e. Lux, Sona, Varus, etc.), however these players rarely get far, as they are KDA machines looking to boost their own ego. A team of Udyr, Xin Zhao, Volibear, Irelia, and Braum likely isn't going to have a fun time against Lux, Sona, Varus, Nidalee, and Ziggs. They will, more often than not, be poked out and sieged into oblivion. That's what makes ARAM fun to most of us, the randomness and off-build team comps/builds. Tank Janna, you say? Sign me up. AP Volibear? Roar them to death! It's also generally a far less toxic game mode, aside from a few outliers, and is great practice to learn every champion. Most people say nothing in ARAM unless it's to congratulate their teammates on a job well done, or "?" Ping when someone does an absolutely astonishing play.
Here's my MMR, for reference: https://na.whatismymmr.com/plscheckthisbush
I've had the luxury of playing against many high-ranking players, including those that play on professional teams. Here's a picture of me playing (and losing) against Challenger Rikara of the team GCU:
http://imgur.com/uSoGPWO