The Pi's GPIO pins are usually not up to the task of driving most mechanical relays and many solid state relays (SSR). Usually you will need some sort of interface between the two.
What is the wattage of the heater you plan to use? I know you said "110V" at somewhere between 8-10 amps, but verifying anyway. I put "110V" in quotes because most people say that for historical reasons (it was what Thomas Edison used originally with his dc system) but modern USA utilities are nominally 120V ~+/-5% (so expect between about 114V to 126V).
Depending on how much you are willing to spend, you could get an SSR for ~$27 usd that could be driven directly off the Pi GPIO and also handle the current you want...
https://www.digikey.com/product-detail/ ... -ND/678179
This one must turn on with 3V on its input, so the GPIO out of 3.3V will work directly. However note the data sheet shows an input current of "3 - 25mA (240 model)" which means if you are going to buy just one, you will want to test it and make sure its input current is less than 16mA, the max of the Pi's GPIO. If on the other hand you were going to be making a lot of these (like for a product) where you were not going to test the input current, then this one is not suitable as many might exceed the 16mA spec. Also note that this type of relay typically requires an additional heatsink for the higher currents.
For just under $34 usd there is this one...
https://www.digikey.com/product-detail/ ... ND/2330435
which is much like the one above but the input current is spec'd to be no more than 14mA so safe to use, although its minimum current is about 10mA, so may not be as low as the one above. The heatsink advise above still applies here.
If you wanted to go much cheaper then for under $5 you could get something like this in a mechanical relay...
https://www.digikey.com/product-detail/ ... -ND/287569
But the problem with mechanical relays is the coil current is almost always going to exceed the current the GPIO can deliver, so you will need to drive the relay with something else. The one I liked it a 12V coil so you would need to drive a relay driver with the Pi's GPIO to turn on the relay's 12V coil voltage which will mean a small IC or converter board. Do you solder? You won't need a heatsink though.