This paper is concerned with the problem of statistical hypotheses testing in circular data under weighted sampling. The most powerful test has been obtained when the sampling is subjected to a weight function. Different weight functions are examined for the von Misses distribution. For the same weight function, the critical values and the power of the test can be calculated analytically, and for some, we need to use a numerical method. The simulation study shows that the power of the test increased as the weighted circular distribution is considered in replace of the original circular distribution and the sample data increased. A real-data example has been carried out to show the performance of our method.