Verify that your internet connection is working. Siri depends on an internet connection (cellular data or Wi-Fi data) to operate correctly. If your internet connection checks out, it could be a fault with Apple's servers (which Siri operates from). Maybe try again later.
You can also try resetting (you won't lose any content or settings) the phone:
Press & hold (continue to hold) both the Home and Lock Screen (power) buttons until you see the Apple logo. Then release both buttons & allow the phone to start normally.
No Siri is working fine setting reminders for me.
Have you tried restarting or resetting your iPhone?
Restart: Press On/Off button until the Slide to Power Off slider appears, select Slide to Power Off and, after the iPhone shuts down, then press the On/Off button until the Apple logo appears.
Reset: Press the Home and On/Off buttons at the same time and hold them until the Apple logo appears (about 10 seconds). Ignore the "Slide to power off"