  We introduce the fractional version of oriented coloring and initiate its
study. We prove some basic results and study the parameter for directed cycles
and sparse planar graphs. In particular, we show that for every $\epsilon > 0$,
there exists an integer $g_{\epsilon} \geq 12$ such that any oriented planar
graph having girth at least $g_{\epsilon}$ has fractional oriented chromatic
number at most $4+\epsilon$. Whereas, it is known that there exists an oriented
planar graph having girth at least $g_{\epsilon}$ with oriented chromatic
number equal to $5$. We also study the fractional oriented chromatic number of
directed cycles and provide its exact value. Interestingly, the result depends
on the prime divisors of the length of the directed cycle.
