Why is charge not taken as a fundamental unit? According to the definition of electric current, it appears to be a derived quantity. Charge on the other hand seems more fundamental than electric current.  Then why is current taken as fundamental quantity instead of charge? 
Is it arbitrary choice? Is it because we can measure current more efficiently than charge or some other reason?
 A: I think that the question is why the SI system of units considers one ampere, the unit of current, to be the elementary one, rather than the unit of the electric charge. 
Recall that one ampere is defined in SI as

"the constant current that will produce an attractive force of $2\times 10^{–7}$ newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum"

Note that this definition relies on magnetic forces; it is equivalent to saying that the vacuum permeability 
$$\mu_0=4\pi\times 10^{-7} {\text{V s/(A m)}} $$ 
It's the magnetic force that has a "simple numerical value" in the SI system of units, and magnetic forces don't exist between static electric charges, just between currents.
If we tried to give a similar definition for the electric charge, using the electrostatic force, the numerical values would be very different.
Now, one may ask why the magnetic forces were chosen to have "simple values" in the SI system. It is a complete historical coincidence. The SI system was designed, up to the rationalized additions of $4\pi$ and different powers of ten, as the successor of CGSM, the magnetic variation of Gauss' centimeter-gram-second (CGS) system of units.
These days, both methods would be equally valid because we use units in which the speed of light in the vacuum is fixed to be a known constant, $299,792,458\,{\rm m/s}$, so both $\mu_0$ and $\epsilon_0=1/(\mu_0 c^2)$, the vacuum permittivity, are equal to known numerical constants, anyway.
At any rate, the unit of the electric charge is simply "coulomb" which is "ampere times second", so it is as accurately defined as one ampere.
