A　stochastic　mathematical　program　model　with　second-order　cone　complementarity　constraints　(SSOCMPCC)　is　introduced　in　this　paper.　It　can　be　considered　as　a　non-trivial　extension　of　stochastic　mathematical　program　with　complementarity　constraints,　and　could　arise　from　a　hard-to-handle　class　of　bilivel　second-order　cone　programming　and　inverse　stochastic　second-order　cone　programming.　By　introducing　the　Chen-Harker-Kanzow-Smale　(CHKS)　type　function　to　replace　the　projection　operator　onto　the　second-order　cone,　a　smoothing　sample　average　approximation　(SAA)　method　is　proposed　for　solving　the　SSOCMPCC　problem.　It　can　be　shown　that　with　proper　assumptions,　as　the　sample　size　goes　to　infinity,　any　cluster　point　of　global　solutions　of　the　smoothing　SAA　problem　is　a　global　solution　of　SSOCMPCC　almost　surely,　and　any　cluster　point　of　stationary　points　of　the　former　problem　is　a　C-stationary　point　of　the　latter　problem　almost　surely.　C-stationarity　can　be　strengthened　to　M-stationarity　with　additional　assumptions.　Finally,　we　report　a　simple　illustrative　numerical　test　to　demonstrate　our　theoretical　results.