Can arts background students apply for jobs in banks?

It depends upon the type of requirement and vacancy. If there are vacancies in Marketing, Sale or PR then having Arts background is a better choice rather than commerce.

Hi Abhijit Only fine arts majors hv some restrictions otherwise you are eligible for all jobs like SSC, Customs, excise, banks,ias, ips etc. Just prepare well for your PO exams and you can go places. All the best

All graduates are eligible for Government Bank PO and clerical roles. You can apply. It is recommend that you work on your analytical and numerical abilities to improve your chances of success. Private banks now days prefer MBA for majority of jobs with them.