Touch-based object recognition relies on perception of compositional tactile features like roughness, shape, and surface orientation. However, besides roughness, it remains unclear how these different tactile features are encoded by neural activity that is linked with perception. Here, we establish a cortex-dependent perceptual task in which mice discriminate tactile gratings on the basis of orientation using only their whiskers. Multielectrode recordings in the barrel cortex reveal weak orientation tuning in average firing rates (500-ms time scale) during grating exploration despite high levels of cortical activity. Just before decision, orientation information extracted from fast cortical dynamics (100-ms time scale) more closely resembles concurrent psychophysical measurements than single neuron orientation tuning curves. This temporal code conveys both stimulus and choice/action-related information, suggesting that fast cortical dynamics during exploration of a tactile object both reflect the physical stimulus and affect the decision.