Yes, fortunately, a lot of sleeping bags in the market could take a few spins in the washing machine. However, it is best to use a front-loading washer (or top-loading machine without an agitator) instead of a regular top-loading washing machine. Please be advised, though, that some home front-loader machines are usually small and would not give your sleeping bag enough space to tumble and clean properly.
Also, make sure to wash the bag in a gentle cycle, using an appropriate soap for this purpose. Using regular laundry soap does more harm than good to your sleeping bag, since too much suds could take a longer time to rinse and therefore causes more aggression on the down inside.
Moreover, help balance out the load of the washing machine by adding a few items like a couple of towels or a few t-shirts that also needed cleaning.
Rinse your sleeping bag at least twice to make sure that all soap residues are gone, or you could also put the bag through a complete wash (soap-free) and rinse cycle.