Yes, there are a number of services available - you should probably be searching for "load testing service".
I'll point out the free version of our product: Load Tester LITE. The LITE version provides testing of simple scenarios for free with no limit on the number of simulated users, but the use of our cloud engines to generate the load is not free (you can use your own hardware to generate load, if you like, for free). There are other restrictions as well.