A Welsh schoolboy international, Curtis was playing amateur football with Cardiff Corinthians, also working as an electrician, when he joined Cardiff City in 1925. On his signing, he was initially an amateur with the side and featured in the reserve team before being offered his first professional contract in 1926. He made his senior debut for Cardiff on 25 September 1926 in a 2–0 defeat to Manchester United, replacing Potter Smith in the starting lineup. In the following match, he scored his first goal for the club during a 6–3 defeat to Derby County. He featured more than 30 times in all competitions during his debut season, which was also limited by an ankle injury sustained in March 1927. As a result he missed the club's FA Cup semi-final victory over Reading, as well as six league matches.