An RC parachute usually has a small engine, hence its full name, the RC powered parachute.
These things really belong in the 'powered soaring' category. They are not really powered RC models in the usual sense because they don't totally rely on the engine. After using the engine to launch, some of these model powered parachutes are capable of fairly long flights using thermals. Just like an RC sailplane or glider.
The size of these models varies a lot. Everything from 1/16th to 1/2 scale has been flown! Half scale?! That's almost enough to give lil' ol' granny the experience of her long lifetime... ;-)
Nearly every model paraglider I have come across is really an RC powered parachute. The power, just like in other model aircraft, is either a small 2-stroke engine or an electric motor. As well, there are a few monster sized models out there that use a variety of other, bigger engines. For example, chain-saw engines! Also, some of the larger model aircraft engines are 4-strokes.
The 2-stroke 'gas' engines, as Americans like to call them, have the advantage of long duration. Your flight time under power is only limited by the size of the fuel tank. Others prefer the much quieter electric motors, but flight times are limited by how many heavy batteries can be carried. It'll be a while before an electric RC parachute can stay up just as long as the petrol-powered variety.
Kits are available for these aircraft. At one end of the scale, several hours of work are required to get the craft in the air. If you are prepared to shell out much more money, the package arrives almost ready-to-fly.
As with most model aircraft, the bottom end of the price range will just get you a plastic toy!
But I guess even one of these could be fun to fly while para-waiting. There's one in particular that seems to be everywhere, and that's the Sky Surfer RC paraglider. It's sold under a few other names too. The gondola and wing are plastic, the motor is electric and it needs fairly calm conditions. If the wind strength is over 16 kph (10mph) then things get difficult. The prices for these models are in the 10s of US dollars, particularly the second hand ones on eBay!
Since the year 2000 or so, a few hobbyists have been keen enough to construct and fly their own RC parachute design. Most just use power kites rigged with a container for the radio gear. Plus a motor in some cases. I don't know how successful these units are, but there was at least one case of a guy using a scaled-down version of a full-size PPG wing. Hard to build accurately, but that would surely be the way to go, for the best chance of success!
There's at least one hobbyist whose designs fly well enough for him to sell them over the Web. He has been doing it for many years, and has the satisfaction of knowing that many units hand made by himself are flying at various locations all around the world. He offers 3 different sizes, and sells the units as kits. Various options are available, catering for people who might have time but not much money or the other way around!
It's funny how some modelers just have to operate huge models! I came across one example of someone flying a 1/3 scale paralider equipped with a modified lawnmower engine! It must have had a lot of wing area compared to its overall weight, since it apparently flew at about 17 kph (11 mph)! That's only a fraction faster than the much smaller Sky Surfer toy. A real 'floater', that RC parachute.
For those that are for sale, these model aircraft are worth several hundred US dollars.