Your best bet would be something like the
Hoya Pro-1 77mm UV filter. It's designed for minimum vignetting on wideangle lenses by using a thin frame, but I believe that it does have enough front threads to hold a lens cap.
The
Canon EF-S 10-22/3.5-4.5 USM isn't particularly sensitive when it comes to vignetting with filters. However with a "normal" thickness Tiffen circular polarizer I did see some vignetting at 10mm. You might get away with a "standard" thickness UV filter, though I'd still recommend the Pro-1 I linked to above. If you're looking for a polarizer that doesn't vignette though, you'd certainly be well advised to go for one of the low profile types such as the
Hoya 77mm DMC PRO1 Circular Polarizer.
For lenses that are very prone to vignetting, Hoya make a special low profile polarizer with no front filter threads, the
Hoya 77mm Extra Thin SMC Circular Polarizer , however it's more expensive, won't take the clip-in lens cap and probably isn't necessary for the EF-S 10-22.