How to power down a Peripheral

I have a 328p and an attached serial communicator.
This communicator can not be put into sleep.
The communicator has 4 wires, RX, TX, VCC and GND.

My thought was to connect the VCC to one of the digital pins (pin 7),
the GND to the GND pin and after bringing the digital pin to
LOW state, the communicator should shut down.
This does not happen. Voltage on pin 7 stays around 1,2V, current around 45mA.
Changing it to LOW or HIGH does not change anything.

Any thoughts?

If the serial communicator uses more than 5mA, it is a bad plan to power it from an Arduino output pin. Power it from an external transistor and control the transistor with the Arduino.