According to diagram in the question, magnetic field at the centre $C$ will be sum of the magnetic field due to straight part $B_1$ and magnetic field due to rircular part $R_{2}$ $\because$ From Maxwell's right hand thumb rule direction of both magnetic field at the point $C$ will be same and above the plane of paper.
So, $B_{C}=B_{1}+B_{2}=\frac{\mu_{0} i}{4 \pi r}+\frac{\mu_{0} i}{4 r}=\frac{\mu_{0} i}{4 \pi r}(1+\pi)$
Hence, the magnetic field at the centre $C$ of the arrangement shown in figure is, $\frac{\mu_{0}}{4 \pi r} i(1+\pi)$.
