Bridgend-born Baldwin began his professional career with local team Bridgend Ravens, before signing his contract with the Ospreys in January 2009.

[8] Prior to an Ospreys rugby union match against Cheetahs in September 2017, Baldwin was bitten on the hand by a captive lion at Weltevrede Game Lodge near Bloemfontein, South Africa.

[9][10] Ospreys coach Steve Tandy described Baldwin's conduct as "pretty stupid", and added "I don't know what sort of wildlife show Scott has been watching where you can pat a lion on the head as if it's a kitten.

[13] Baldwin was selected in the Wales squad for the 2015 Rugby World Cup, and started every match, scoring a try against Fiji in the pool stages.

[17][18] On 24 January 2023 Baldwin earned a recall to the Welsh squad, his first selection in more than five years, having been called up to replace the injured Dewi Lake for the 2023 Six Nations.