I would like to know how to calculate torque required to turn an plastic extruder screw 120mm in dia and 3.6mt in length at 70 rpm. Material conveyed by screw (which is inside a barrel) is high density polyethylene of MFI 0.1.

This isn't a simple torque calculation (length of arm times force), nor is the calculation easy. I'm not even sure I know all of what's required to do it. You need to know the cross-section of the extrusion die, lengths of the extrusion path, etc. Engineers do these types of calculations. Maybe you could re-post your question under engineering (though I don't think a lot of engineers post there).