If you haven't a high-speed camera, you can calculate indirectly. The wetted surface area is different in color. If you know the volume of the drop and the diameter of this wetted surface area, you can calculate it here because the diameter of the cut sphere will be the diameter of the wetted area.

Thanks a lot for your response. But how will this diameter be utilized for calculating contact angle?

The volume of a spherical drop is determined. We produced a 1 microliter volume drop, which is 1 cubic mm volume. Likewise, the volume of the cut sphere formed after dropping is 1 cubic mm. We now know the volume of the cut sphere, and when we measure the cross-sectional diameter from the trace at the dropped location, we can now calculate the contact angle by going from the cut sphere formula. Drop penetrate to the object through first contact area.

Thanks for this insight. Also, we do have a high speed camera but generally we measure the contact angle after the solvent is in equilibrium with the surface. In the above mentioned case it doesn't happens? Is it the only method left then?

Follow the angle measurement until the drop is formed at the tip of the syringe and is contacted and sucked to the surface. I understand that the drops you produce are absorbed before they form on the surface in the form of a cut sphere. If the drop absorption is much faster than the speed of your camcorder, a drop image will not appear indicating a contact angle. Other surface tension measurement methods may be required. Or add adjuvants to your fluid that slow down absorption.