If an expatriate worker gets citizenship in Bahrain, can he get a pension?

Yes, because they will be subject to the Social Insurance Law.

I assume you meant retirement pension?

If so, entitlement to the same depends on registration with the SIO and payment of the monthly fees.

There are requirements as to the minimum amounts and the length of service/payments.

Citizenship will not grant you a pension if you were never registered or paid the fees.