Most true ferns are non-toxic to our indoor furry four-legged family members. Plants like the asparagus ferns are not true ferns and are toxic to pets.
However, whenever bringing any plant indoors around pets, always do your research to triple-check that your plant is pet friendly.
Even if your plant should be safe for your pet, a good thing to do is still discourage chewing and ingestion of any plant or plant leaves. What should be non-toxic can still cause common GI upset for any pet if it does not agree with their tummy.