Mathematically we can answer the question as:
emf induced in an inductor is: -Ldi/dt thus if
i = I sinwt
then emf induced will be -Lw coswt = Lw sin(pi/2 + wt)
Thus current lags behind emf by pi/2
also physically it can be understood as:
According to lenz's law, the emf induced will be so as to compensate the change in current.
Thusas the current in the coil increses the emf across it decreases, thus the current lags by a phase difference of pi/2