Yes, It's called Run and Gun or RnG for short.
These are 5K, 10K or even 20K races with shooting stages, usually between 5 and 8 stages.
They are fun, and will test your skills and fitness. Many course incorporate obstacles to negotiate along the way.
They are a true test of your skills. Nothing like shooting targets out to 500 yards, from an unconventional position when your heart rate is around 160 bpm!!
These events are springing up all over the south and east. I'll do at least 6 a year, but if you're willing to travel, you can do more.
Check out one of the more popular events here.
Another popular one