You mean the magnetic flux through the middle of the coil (called a solenoid)? Yes, it increases if you increase the electric current through wire.
A lot of times the easiest way to see "what happens" is to take a process to a ridiculous proportion. For example, "what happens to magnetic flux if you decrease the electric field of a solenoid" can be answered by the question "what happens to the flux if you decrease the field all the way to 0, that is, turn off the electric field. Obviously the magnetic flux disappears. So yes, making your electric field get closer to 0 makes your magnetic flux get closer to 0 (this doesn't actually logically follow and a mathematician would want proof that the function relating the field to the flux is monotone increasing/decreasing and continuous for example but its good enough for some intuitive stuff).
So yeah, increasing the current increases the flux.