Yes. You can sue the bar if the stairs were defective or dangerous. The bar has a duty to keep the stairs safe for its "invitee" or someone who's been invited onto the premises. You would be an invitee, and patrons of the bar would also be considered as invitees.
If the shaky stairs were dangerous and/or defective in some way and the bar owner(s) neglected to fix them, then you can bring a claim against the bar. In order to prove that the stairs were defective or dangerous, an inspection of the stairs would need to be conducted.
However, there are also other legal elements we would need to prove, such as notice. Click here to see related articles about notice in a slip and fall accident case:
Please keep in mind that my answer is based on the limited information contained in your question. Feel free to contact me to discuss the details of your unfortunate fall so I can properly evaluate your case. 877.944.8396