Can rasps be grown in pots?

They can, but unless they're largish pots, I wouldn't recommend it. They tend to dry out quickly in drier weather and their natural tendency to send runners will quickly make them potbound.

My friend grow's raspberries and strawberries on a commercial scale. All the raspberries are in 10 inch pots and are fed and watered by an automatic irrigation system. They are thrown out after 2 year's and replaced with new stock. The strawberries are grown in growbags and also have the automatic irrigation system. They are thrown out after 3 year's. It is cheaper for him to but in new stock rather than potting up the runner's. In answere to your question, Yes you can but there will be a lot of work involved, watering feeding etc.