I am trying to determine the correct institution ABA based on the credit card's BIN. There are several resources which can determine bank's name and some other info based on the card BIN but many banks have multiple routing numbers (e.g. Chase and Wells Fargo). Is it possible to determine a single correct ABA for the account?
I'm assuming the context for your question is a checking account in the US with a debit card, and you know the BIN on the debit card and are trying to determine the ABA routing number for the checking account.
Unfortunately, the answer is no - there is no inherent relationship between BIN and routing number, and there are inconsistencies from bank to bank because of differences in the way financial institutions are structured. For instance, some larger banks may have different routing numbers for accounts opened in different regions, but only one BIN that they use for all cards. Other banks may have only one ABA for all checking accounts, but different BIN numbers for different card products attached to different types of accounts. Still other institutions will have only one routing number and one BIN.
If you are a customer of the bank, you can just call and ask, or look on their website (many online banking portals display the routing number prominently - for my bank, it's at the bottom of every page). If you are not the customer, and the only piece of information you have is a BIN, you are effectively out of luck. You can always try calling the bank and asking - if they have only one routing number, they will tell it to you. But if the bank has multiple routing numbers, they may need you to give them other information in order to provide you the correct number (such as, which state the account was opened in).