Yes.
Ikelite make a rigid housing for it - couple of links;
http://www.bristolcameras.co.uk/p-ikelite-underwater-housing-for-canon-powershot-sx10-is-sx20-is.htm
http://www.camerasunderwater.co.uk/d_stills/canon/ike_sx--.html
You will almost certainly need a strobe (flash unit) as well, as you won't be using any 'onboard' flash. If you use the Ikelite DS series substrobes, you have full TTL control. As someone else hinted at, underwater photography isn't cheap!! It will be cheaper to buy a second (cheaper) compact & housing than to kit out your SX20, however, the IQ from compacts isn't great u/w and they tend to have too much shutter lag.
You should try out any housing you get in a pool first before you venture into the sea, firstly without the camera in it. Check and press all the buttons/knobs numerous times & check for leaks. Then try it out with the camera in & take a few test shots in the pool.
I can thoroughly recommend Martin Edge's book too (new edition just out);
http://www.amazon.co.uk/Underwater-Photographer-Martin-Edge/dp/0240521641/ref=sr_1_1?ie=UTF8&s=books&qid=1270380069&sr=1-1
The cardinal rules when shooting underwater are to get close & shoot upwards (if possible).
The best advice I can give is to look after the O rings - they should be checked, re-greased & seated properly before every dive session. Any grit, hair, dust, sand, nicks & cuts on the O ring can potentially cause leaks & a flood then its bye bye camera!! Use the recommended O ring lube, not the usual silicone grease you'd use for other dive gear. If the camera does flood catastrophically during a dive, don't rush to the surface. It's too late by then & you'll risk a bend. If you see a small leak & it's salvageable, then point the camera downwards (so any water collects in the lens port area - less damage) & surface as per deco schedule.
Enjoy!
Edit: Martin G may not be correct. You may not need weights for neutral buoyancy - depends. My Nikon DSLR in a Sea & Sea housing with dual strobes weighs a ton on land but u/w its perfectly neutrally buoyant with no weights.