You'd need to provide more info on how you set up the camera to use the external flash. Although the 600Ex-RT can work in "radio" mode, the 70D doesn't have a radio transmitter -- it will only work in "optical" mode.
Press the link button on the 600EX-RT (the zig-zag lightning bolt just above the mode button) until you see the lightning icon in the upper right corner of the LCD and the word "slave" (listed below the channel number). You are now in "optical slave" mode.
Meanwhile, back on the 70D... one thing that can be confusing is that when you go into flash settings. When you go into "flash settings" menu, you'll find something for "built-in flash" and something for "external flash" and here's where it gets confusing... "external flash" is used to control a flash like your 600EX-RT only when attached to the on-camera hot-shoe. If the flash is off-camera and being controlled wirelessly, then the "built-in flash" is used to trigger the 600EX-RT. That means you have to go into the "built-in flash" menu to control those features.
Once you are in the "built-in flash" menu, you'll see an option for "Wireless func." and this is where you enable the feature you need. There's an icon of the camera's pop-up flash (in profile) and an icon of the external flash (in profile). There are only four choices:
- disable (don't fire an external flash)
- use internal and external as a ratio (the ":" between the two icons)
- use external only (you will see the internal flash fire... but technically it does this when the shutter is still closed to send messages to the external flash. When the shutter is open only the external flash fires. This all happens so fast you'd swear you just saw one flash but it does flash several times.)
- use internal and external flash as a group in E-TTL or manually if not in E-TTL (the "+" between the two icons.)
See your instruction manual on "Using Wireless Flash" on page 203.
Both camera and flash must be set to the same channel (picking a channel allows you to shoot in locations where other photographers are also using wireless flash without your gear triggering each others' off-camera flashes.)
One more thing... since the external flash is getting it's firing signal optically, the 600EX-RT must be able to "see" the on-camera flash. The sensor is in the front of lower-half of the flash (the part that doesn't swivel). Make sure this is facing the camera. Then swivel the top of the flash to anywhere you'd like to direct the light.
If line-of-sight isn't possible, you'll need to use a radio trigger such as a 2nd 600EX-RT on-camera or the Canon ST-E3-RT on-camera transmitter.