Yes, you can definitely grow raspberries in pots, as well as grapes and a variety of other fruits. For inspiration, take a look at fruitnut's results with potted grapes and blackberries. For good background reading on how to successfully grow plants of all types in pots, check out these two threads in the Container forum...

Container Soils - Water Movement and Retention XVIII

Fertilizering Containerized Plants IV

Here's a photo of my baba raspberries (the two on the right) growing on my patio in San Diego. I'm using 5:1:1 mix in #5 black plastic pots in decorative cache pots.

not cheap but BrazelBerries Raspberry Shortcake

Here is a link that might be useful: BrazelBerries Raspberry Shortcake

Monrovia is also selling the 'RaspberryShortcake'. You might be able to order it locally from a good garden center. Pots may need winter protection so the roots don't freeze (and die).