The midfielder has made just one cameo appearance so far this season after recovering from a fractured leg, which he suffered towards the end of the 2016-17 campaign while on loan at Bournemouth.
Youngster Reiss Nelson has been handed his full debut for the North London outfit, while Ainsley Maitland-Niles also gets the nod from Wenger, who has opted for a three-man defence consisting of Calum Chambers, Per Mertesacker and Rob Holding.
Arsenal: Ospina; Chambers, Mertesacker, Holding; Nelson, Wilshere, Elneny, Maitland-Niles; Walcott, Sanchez, Giroud
Subs: Macey, Monreal, Willock, Dasilva, Iwobi, Nketiah, Akpom
Doncaster Rovers: Lawlor; Blair, Butler, Whiteman, Wright; Kongolo, Mason, Coppinger, Rowe, Houghton; May
Subs: Marosi, Alcock, Toffolo, Garratt, Mandeville, Marquis, Williams