Are power outlets for window A/C units likely to support 220V?
That is a 120v outlet.

220v outlets use different shaped slots - both horizontal instead of vertical. Like this:

The plugs and outlets are made to be incompatible with 120v ones because plugging a device into the wrong voltage outlet could cause serious damage or fire.

IF that is a dedicated circuit for the AC it can be rewired as 240v quite easily by replacing the breaker and wiring it differently at both ends, using the existing wire in the wall.  It will still be limited to whatever amperage the existing run supports - probably 15 or 20 amps depending on the wire gauge.

If other things are on the same circuit you would need to run new wire from the electrical panel.

Assuming you rent the apartment (not a condo that you own) you would usually need the landlord's permission to get it changed.