Let the current be $i$ amperes and radius be $R$.
Take an elementary wire which subtends an angle $d\theta$ at the centre and $\theta$ angle away from the diameter.
Current in that element is $$di=\frac{i.d\theta}{\pi}$$.
Now the magnetic field at the centre will be $$\int \dfrac{\mu_o di \sin(\theta)}{2 \pi R}$$ (along the direction of diameter).
And the magnetic field at the centre will be $$\int \dfrac{\mu_o di \cos(\theta)}{2 \pi R}$$ (along the direction perpendicular to the diameter).
Take the limits of $\theta$ from $0$ to $\pi$. The second integral will evaluate to zero. The value of first integral is the final answer.
P.S: First of all draw a neat diagram and follow the above steps to reach the answer. Use Biot-Savart's law to find the direction of current due to each wire element.