Yes, you can, but it depends on the age, condition of the feather and where you found it and if you have a suppressed immune system. So, there are many variables that control whether you can get sick.

If the feather was dropped on the ground in fecal matter, or was a tail feather, the greater the chance that you might pick up salmonella or e-coli. You would probably start feeling nauseas and vomiting or diarrhea within 8-24 hours.

If the feather came right off the bird and it had been in a pond or other water environment, you could pick up ecoli, salmonella, maybe a parasite, etc. Again, if you had any of these, symptoms would begin to appear in 8-24 hours.

If you immediately spit out the feather and continued spitting for a couple of seconds or washed your mouth out, the chances go down but there still could be a possibility of picking up a bacteria.

Did you intentionally stick the feather in your mouth or was it temporary, such as the wind blowing a feather into your face? In the above scenarios, duration in your mouth would also play a role in the probability of a bacterial or parasitic infection.

Hopefully, this is not to scare you, just the worst case scenario. This is why we constantly warn educators and parents who use feathers for pens and other crafts for children to wash the feathers thoroughly and even place them in bleach to remove bacteria and other possible contaminants. To set your mind at ease and to be extremely cautious, you might want to check with a physician to just to make sure. The Regal Swan