We compute explicitly the Selberg trace formula for principal congruence subgroups $\Gamma$ of $PGL(2, \mathbf{F}_q[t])$, which is the modular group in positive characteristic cases. It is known that $\Gamma \backslash X$ is an infinite Ramanujan diagram, where $X$ is the $q + 1$-regular tres. We express the Selberg zeta function for $\Gamma$ as the determinant of the adjacency operator which is composed of both discrete and continuous spectra. They are rational functions in $q^{-s}$. We also discuss the limit distribution of eigenvalues of $\Gamma \backslash X$ as the level tends to infinity.