The oriented graph coloring game was introduced by \textit{J. Nešetřil} and \textit{E. Sopena} [Electron. J. Comb. 8, Research Paper R14 (2001; Zbl 0982.05049)] as follows: Given an oriented graph \(G=(V,A)\) and a tournament \(T = (C,D)\), two players alternately color vertices of \(G\) with colors from the set \(C\) such that, if \(v \in V\) is to be colored \(\alpha\) and \(w \in V\) has already been colored \(\beta\), then \(vw \in A\) implies \(\alpha\beta \in D\) and \(wv \in A\) implies \(\beta\alpha \in D\); in addition, every directed path of length two must have its endpoints differently colored. The first player wins if, after the game ends, all vertices are colored; the second playes wins if, during the game, some vertices cannot be colored. The oriented game chromatic number of \(G\) is the least \(t\) for which there exists a tournament \(T\) on \(t\) vertices such that the first player has a winning strategy. In this paper, the authors prove that, for fixed integer \(k\), there exists a constant upper bound on the oriented game chromatic number of any partial \(k\)-tree.