The solenoid is not clicking when you turn the key but the starter is reading 12 volts.

Then try replacing the solenoid.

While the negative battery cable is disconnected, clean starter motor and starter solenoid connections. Apply silicone dielectric grease, when finished. Make sure all connections are secure. When installing the starter cable, make sure that the crimped side of the ring terminal is facing out. Reconnect the negative battery terminal last.

If the problem persists, consider replacing the solenoid or installing a completely new starter motor/solenoid. You may also want to check out the ignition switch. Access is easy on Civics and it shouldn't take you long to isolate the problem.