Can a former US president serve as US vice president?

Yes, provided he has served only one term. Under the 12th Amendment "no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United states." Thus a President who has been elected twice (and so under the 22nd Amendment become ineligible to any further terms) would also be disqualified from election as Vice-President. In 1980, Ronald Reagan offered the Vice-Presidency to ex-President Gerald Ford (who declined it). This would have been perfectly legal as Ford had not served two terms. However, a similar offer to ex-President Nixon (who had done so) would have been unconstitutional.