The Cardiff flanker has excelled in the role for his club, and Steve Hansen will give Williams the chance to prove his skills at international level.
Williams won the BT Man of the Series award for his consistent performances in the autumn internationals, and was outstanding against both Italy and England.
He will become Wales' third captain of the Six Nations campaign when he leads the team out at Murrayfield, he follows Colin Charvis, who was dropped after a disappointing show in Italy, and Jonathon Humphreys - skipper for the England match- who has been ruled out because of a shoulder injury.
Hansen has made two changes from the side beaten by England at the Millennium Stadium.
Llanelli fly-half Stephen Jones has recovered from a broken thumb and makes his first start of the championship.
He replaces unlucky Ceri Sweeney, who, despite a competent first start against England, does not find a place in Hansen's 22.
The other switch is an enforced one in the front row, where Bridgend hooker Gareth Williams makes his full Test debut instead of Humphreys.
Former rugby league star Iestyn Harris keeps his place on the bench.
Wales: K Morgan (Swansea), R Williams (Cardiff), M Taylor (Swansea), T Shanklin (Saracens), G Thomas (Bridgend), S Jones (Llanelli), G Cooper (Bath), I Thomas (Llanelli), G Williams (Bridgend), B Evans (Swansea), S Williams (Northampton), R Sidoli (Pontypridd), D Jones (Llanelli), G Thomas (Bath), M Williams (Capt) (Cardiff).
Replacements: M Davies (Pontypridd), G Jenkins (Pontypridd), G Llewellyn(Neath), C Charvis (Swansea), D Peel (Llanelli), I Harris (Cardiff), M Watkins, (Llanelli).