We present a relativistic formulation of pion loop corrections to the coupling of photons with nucleons on the light-front. Vertex and wave function renormalization constants are computed to lowest order in the pion field, including their nonanalytic behavior in the chiral limit, and studied numerically as a function of the ultraviolet cutoff. Particular care is taken to explicitly verify gauge invariance and Ward-Takahashi identity constraints to all orders in the m_pi expansion. The results are used to compute the chiral corrections to matrix elements of local operators, related to moments of deep-inelastic structure functions. Finally, comparison of results for pseudovector and pseudoscalar coupling allows the resolution of a long-standing puzzle in the computation of pion cloud corrections to structure function moments.