You *can* do this, but if your carboys are like anyone else's, then you'll stir up all sorts of trub and crap that will end up in your bottles. The preferred method is to rack from carboy (assuming you're doing primary in it) into a bottling bucket or some other sanitized vessel, then add priming sugars and mix, then rack to bottles.
I wouldn't recommend it.
If you really want to do it though, you shouldn't stir it up since it will just make the beer cloudy and put tons of trub into the bottles. GENTLY start an autosiphon or racking cane with a clamp or having a friend hold it steady so it doesn't disturb the trub on the bottom of the vessel. Get a bottling wand and attach it to the other end of the tubing. While your friend gently gets the suction going and pumps the beer down the tube to the bottling wand. It will need to be in a bottle or something in order for it to work since it wont open unless it is pressed onto the bottom of a bottle or something. Everyone needs to be gentle here or else you'll just pick up trub and/or make a mess on the bottle side! Bottle below the level of the carboy so gravity is always helping, and the person holding the autosiphon/racking cane should always keep it above the trub but below the beer surface in the carboy. Restarting an autosiphon near the bottom of a carboy can be impossible. Keep bottling steadily and have all your bottles ready ahead of time. If you can get through all the bottles without sucking up trub, then congratulations- you've done it. Afterwards, carefully measure about 3/4 tsp sugar per 12oz bottle, or get carb drops from your LHBS.
Or, spend $5.00 on a bucket from Home Depot or something and rack clear beer into that, then mix in priming sugar in bulk (mix it well!), and bottle from there. Much easier, less mess, and no trub.