It is the nature of stockinette stitch to curl. The only way to prevent it is to knit a garter stitch or seed stitch edging--five rows when you start and five stitches at each end of the rows, approximately, depending on the yarn and needle size.
This comes up so often, I think all yarn labels should have a warning label.
It doesn't matter when the piece is going to be seamed, but for scarves without some kind of edge it happens. You could possible add an edge, but that's an awful lot of stitches to pick up.