Many ants use a combination of cues for orientation but how do ants find their way when all external cues are suppressed? Do they walk in a random way or are their movements spatially oriented? Here we show for the first time that leaf-cutting ants (Acromyrmex lundii) have an innate preference of turning counter-clockwise (left) when external cues are precluded. We demonstrated this by allowing individual ants to run freely on the water surface of a newly-developed treadmill. The surface tension supported medium-sized workers but effectively prevented ants from reaching the wall of the vessel, important to avoid wall-following behaviour (thigmotaxis). Most ants ran for minutes on the spot but also slowly turned counter-clockwise in the absence of visual cues. Reconstructing the effectively walked path revealed a looping pattern which could be interpreted as a search strategy. A similar turning bias was shown for groups of ants in a symmetrical Y-maze where twice as many ants chose the left branch in the absence of optical cues. Wall-following behaviour was tested by inserting a coiled tube before the Y-fork. When ants traversed a left-coiled tube, more ants chose the left box and vice versa. Adding visual cues in form of vertical black strips either outside the treadmill or on one branch of the Y-maze led to oriented walks towards the strips. It is suggested that both, the turning bias and the wall-following are employed as search strategies for an unknown environment which can be overridden by visual cues.