If ray OC is the angle bisector of angle AOB, it divides the angle AOB into two equal parts. The measure of angle AOB is given as 84 degrees.
To find the measure of angle AOC, we can divide the measure of angle AOB by 2:
\[ \text{Measure of angle AOC} = \frac{84^\circ}{2} = 42^\circ \]
Thus, the measure of angle AOC is \( \boxed{42} \) degrees.