Yes biting your fingernails can be a sign of anxiety.
Biting your fingernails is a common sign of stress as well as anxiety and most people who do have anxiety or are stressed may bite their fingernails as a way to calm themselves down.
Some people bite their fingernails out of boredom and some people bite their fingernails because of stress and anxiety.
If you're nervous about something then that could be a reason of biting your fingernails too.
If you think you're suffering from anxiety and are constantly biting your fingernails you should see a doctor and let them know about your anxiety.
The doctor can get you on some anxiety medicine to help you calm down so that you don't have to bite your fingernails.
Sometimes biting your fingernails may just be a habit that you get.
I used to bite my fingernails a lot in school and even chew on erasers, pencils, my hair and even chew on my shirt.
As a 4 year old and up until about 8 years old I would chew on my shirt but not sure why.