Contextual information can have a huge impact on our sensory experience. The tilt illusion is a classic example of contextual influence exerted by an oriented surround on a target's perceived orientation. Traditionally, the tilt illusion has been described as the outcome of inhibition between cortical neurons with adjacent receptive fields and a similar preference for orientation. An alternative explanation is that tilted contexts could produce a re-calibration of the subjective frame of reference. Although the distinction is subtle, only the latter model makes clear predictions for unoriented stimuli. In the present study, we tested one such prediction by asking four naive subjects to estimate three positions (4, 6, and 8 o'clock) on an imaginary clock face within a tilted surround. To indicate their estimates, they used either an unoriented dot or a line segment, with one endpoint at fixation in the middle of the surround. The surround's tilt was randomly chosen from a set of orientations (±75°, ±65°, ±55°, ±45°, ±35°, ±25°, ±15°, ±5° with respect to vertical) across trials. Our results showed systematic biases consistent with the tilt illusion in both conditions. Biases were largest when observers attempted to estimate the 4 and 8 o'clock positions, but there was no significant difference between data gathered with the dot and data gathered with the line segment. A control experiment confirmed that biases were better accounted for by a local coordinate shift than to torsional eye movements induced by the tilted context. This finding supports the idea that tilted contexts distort perceived positions as well as perceived orientations and cannot be readily explained by lateral interactions between orientation selective cells in V1.