Answer
The magnetic field at $C$ is into the page.
Work Step by Step
Note that the straight sections of wire do not produce any magnetic field at $C$
We can write the expression for the magnetic field due to an arc of current:
$B = \frac{\mu_0~i~\phi}{4~\pi~R}$
We can find the magnetic field at $C$ due to the arc of current with radius $R= 9.26~cm$:
$B = \frac{\mu_0~i~\phi}{4~\pi~R}$
$B = \frac{(4\pi\times 10^{-7}~H/m)~(0.0348~A)~(\pi~rad)}{(4~\pi)~(0.0926~m)}$
$B = 1.18\times 10^{-7}~T$
By the right hand rule, the magnetic field at $C$ is into the page.
