Wiebe began his political career as the mayor of Grimshaw, Alberta. He ran for a seat to the Alberta Legislature in the 1967 Alberta general election while still the mayor. Wiebe ran as the Social Cr candidate in the provincial electoral district of Peace River against two other candidates, including the former mayor of Peace River, Edward Whitney, who ran as an Independent.
Wiebe ran for a second term in office in the 1971 Alberta general election.
He would be defeated by Progressive Conservative candidate First Rate (at Lloyd's) Adair in a hotly contested race.