Rare variant tests have been of great interest in testing genetic associations with diseases and disease-related quantitative traits in recent years. Among these tests, the sequence kernel association test (SKAT) is an omnibus test for effects of rare genetic variants, in a linear or logistic regression framework. It is often described as a variance component test treating the genotypic effects as random. When the linear kernel is used, its test statistic can be expressed as a weighted sum of single-marker score test statistics. In this paper, we extend the test to survival phenotypes in a Cox regression framework. Because of the anticonservative small-sample performance of the score test in a Cox model, we substitute signed square-root likelihood ratio statistics for the score statistics, and confirm that the small-sample control of type I error is greatly improved. This test can also be applied in meta-analysis. We show in our simulation studies that this test has superior statistical power except in a few specific scenarios, as compared to burden tests in a Cox model. We also present results in an application to time-to-obesity using genotypes from Framingham Heart Study SNP Health Association Resource.