It is noted that work in riba-based bank is a debatable issue; some scholars like Dr. Monzer Kahf deem it allowable to work in a riba-based bank as long as the work does not involve riba contracts or dealings, such as working as technical support engineer for the bank computers and the like.
In his answer to the question Dr. Monzer Kahf, Scholar in Islamic Economics & Financial Expert, who stated,
Yes, but provided that you do not work as a writer or signatory of processor of a riba based contract.
The source of income of the bank does not matter to you as long as you give your time honestly and the bank’s funds are not coming from theft of shameful actions.
May Allah guide all of us to what pleases Him!