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Desert ants are expert navigators, foraging over large distances using visually guided routes. Recent models of route following can reproduce aspects of route guidance, yet the underlying motor patterns do not reflect those of foraging ants. Specifically, these models select the direction of movement by rotating to find the most familiar view. Yet scanning patterns are only occasionally observed in ants. We propose a novel route following strategy inspired by klinokinesis. By using familiarity of the view to modulate the magnitude of alternating left and right turns, and the size of forward steps, this strategy is able to continually correct the heading of a simulated ant to maintain its course along a route. Route following by klinokinesis and visual compass are evaluated against real ant routes in a simulation study and on a mobile robot in the real ant habitat. We report that in unfamiliar surroundings the proposed method can also generate ant-like scanning behaviours.