What is the dependence of current through inductor in parallel RLC CIRCUIT with a AC source at resonance frequency
In which condition the current through the inductor approach INFINITY
  and how can you explain that physically?


Yes, it is absolutely true - the current in the inductor can become infinite and the current in the capacitor can also become infinite however, because these two currents are anti-phase (one lags the sinewave source by 90deg and one leads the sinewave source by 90deg), the net current taken from an AC voltage source is zero other than what is consumed in the parallel resistor.

You are using a current source and the resultant voltage will be I*R. I'm also presuming you meant R to be a positive resistance value not as shown in your diagram although that won't alter things at all - if you meant R to be negative then the voltage developed across the resistor will be anti-phase to the current through it.

The actual current through the inductor is the voltage across it (as developed by the resistor and current source). Ditto the capacitor.