The 26-year-old Saracens player steps up from the bench to partner Mark Bennett in Cardiff after Mark Scott was ruled out after suffering a thigh injury in training.
It will be his first start for Scotland since the tour of the U.S. in 2014.
Scotland, beaten 15-9 by England, are trying to avoid a ninth consecutive Six Nations loss, a sorry run that began in 2013, but Cotter said there were some positives last weekend.
"We created opportunities that could have been capitalised upon, and converted into points," he said in a statement announcing the team on Thursday.
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"This group have worked exceptionally hard this week to improve their accuracy under pressure after a frustrating opening game against England.
"We know that Wales in Cardiff will not be easy but our focus is on improving our attacking and defensive mindset."
Team: Stuart Hogg (Glasgow Warriors), Sean Maitland (London Irish), Mark Bennett (Glasgow Warriors), Duncan Taylor (Saracens), Tommy Seymour (Glasgow Warriors), Finn Russell (Glasgow Warriors), Greig Laidlaw (Gloucester); Alasdair Dickinson (Edinburgh Rugby), Ross Ford (Edinburgh Rugby), Willem Nel (Edinburgh Rugby), Richie Gray (Castres), Jonny Gray (Glasgow Warriors), John Barclay (Scarlets), John Hardie (Edinburgh Rugby), David Denton (Bath Rugby).
Replacements: Stuart McInally (Edinburgh Rugby), Gordon Reid (Glasgow Warriors), Zander Fagerson (Glasgow Warriors), Tim Swinson (Glasgow Warriors), Blair Cowan (London Irish), Sam Hidalgo-Clyne (Edinburgh Rugby), Duncan Weir (Glasgow Warriors), Sean Lamont (Glasgow Warriors).
(Reporting by Martyn Herman; editing by Justin Palmer)
