Jenkins first played rugby as a school boy, representing Bryndu School in Kenfig Hill. A keen sportsman as a youth, he also enjoyed association football and had trials with Swansea AFC. After leaving school he joined local club Kenfig Hill, but by the time he was selected to represent Wales in 1926, he had switched to Rhondda team, Treorchy. His first international appearance was in the opening Wales game of the 1926 Five Nations Championship; played against England at the Cardiff Arms Park. The game ended in a 3–3 draw, but Jenkins had done enough to secure his place with the Welsh selectors, and was chosen for the three remaining games of the Championship: a loss away to Scotland, followed by wins over Ireland and France. It is unknown if Jenkins would have been selected for any further rugby union internationals as in August 1926 he switched codes, becoming a professional rugby league player with Hunslet.
Dai Jenkins won three caps for Wales while at Hunslet, his first on 26 April 1927 in an encounter with England at Broughton. This was followed by another two caps in 1928 and 1931, both games against England. The 1928 match, played at Cardiff, saw Jenkins score a try, the only international points of his career. In 1931 he switched from Hunslet to Leeds, and in 1932 won his final cap for Wales, in his fourth encounter with England, and all resulting in losses for Wales. In 1934 he moved clubs again, switching from Leeds to Dewsbury.