Having previously represented Wales at youth and under-23 levels, Dwyer received his first call-up to the senior Wales side in April 1978. Usually a defender, his first selection coincided with a period in which he was playing as a forward for Cardiff. He made his international debut for Wales as a forward against Iran in Tehran on 18 April 1978 at the age of 24. He scored the only goal of the game during a 1–0 win for Wales as well as having a second goal disallowed and hitting the post with another effort. Dwyer was recalled for Wales' following match and scored again during a 3–1 defeat to England in the 1978–79 British Home Championship at his home club ground, Ninian Park, after heading in from a cross by Carl Harris.