Somatic mutations drive the growth of tumor cells and are pivotal biomarkers for many cancer treatments. Genetic association analysis using somatic mutations is an effective approach to study the functional impact of somatic mutations. However, standard regression methods are not appropriate for somatic mutation association studies because somatic mutation calls often have non-ignorable false positive rate and/or false negative rate. While large scale association analysis using somatic mutations becomes feasible recently-thanks for the improvement of sequencing techniques and the reduction of sequencing cost-there is an urgent need for a new statistical method designed for somatic mutation association analysis. We propose such a method with computationally efficient software implementation: Somatic mutation Association test with Measurement Errors (SAME). SAME accounts for somatic mutation calling uncertainty using a likelihood based approach. It can be used to assess the associations between continuous/dichotomous outcomes and individual mutations or gene-level mutations. Through simulation studies across a wide range of realistic scenarios, we show that SAME can significantly improve statistical power than the naive generalized linear model that ignores mutation calling uncertainty. Finally, using the data collected from The Cancer Genome Atlas (TCGA) project, we apply SAME to study the associations between somatic mutations and gene expression in 12 cancer types, as well as the associations between somatic mutations and colon cancer subtype defined by DNA methylation data. SAME recovered some interesting findings that were missed by the generalized linear model. In addition, we demonstrated that mutation-level and gene-level analyses are often more appropriate for oncogene and tumor-suppressor gene, respectively.