Magnesium diboride ($MgB_2$) is an inexpensive and simple superconductor. This material was first synthesized and its structure confirmed in 1953 but its superconducting properties were not discovered until 2001 when they caused great excitement. In this study, superconducting $MgB_2$ thin films on the r-$Al_{2}O_3$ substrates have been grown by the combination of radio frequency magnetron sputtering of B and thermal evaporation of Mg. The deposition conditions were varied by changing deposition rate. Before the co-deposition of Mg and B, the deposition rates of each element have been measured separately. The $MgB_2$ layers had 400nm in thickness and superconducting transition temperatures have been measured around $sim$38.6K. Superconducting properties have been measured by PPMS, XRD, and SEM.