<p>This paper studies mathematical programs with second-order cone complementarity constraints (SOCMPCCs), which generalize classical mathematical programs with complementarity constraints by incorporating second-order cone structures. SOCMPCCs present substantial theoretical and computational challenges because standard constraint qualifications, such as Robinson’s condition, are violated at every feasible point. This prevents the direct application of classical nonlinear programming theories and algorithms. To address these difficulties, we develop a class of smoothing methods that approximate the original SOCMPCC using suitably constructed smoothing functions. We prove that any sequence of stationary points of approximate problems converges to a C-stationary point of the original SOCMPCC under a newly introduced constraint qualification, named SOCMPCC-WLICQ. This condition is proven to be strictly weaker than the widely assumed SOCMPCC-LICQ, yet strictly stronger than the SOCMPCC nondegeneracy condition. Furthermore, we demonstrate that the resulting C-stationary point can be strengthened to an S-stationary point when an additional strict complementarity condition is satisfied. Numerical experiments further verify theoretical results and illustrate the effectiveness of the proposed smoothing methods, as evidenced by their improved performance on several test problems.</p>