Torque, Current and Voltage Relationship in Induction Motor
For me something proportional to square of volt should be proportinal to square of current as well. Is that right?


That is correct if the "something" is governed by Ohm's law. Only resistors are strictly subject to Ohm's law.


  This source may be meaning under constant voltage torque is proportional to current?


Yes. The source must be saying that and a bit more.

The torque capability of an induction motor is proportional to the square of voltage over some range above and below the rated voltage.

The operating torque of a motor is the torque where the torque capability curve of the motor intersects the torque demand or requirement curve of the load. Assuming that the motor is operating below or only a little above its rated torque for continuous operation, the current at the steady-state operating point is proportional to torque.