As Joan suggested 3.3V shouldn't damage the display. However I did find a datasheet for a 1602A which suggests it is a 5V display: https://www.openhacks.com/uploadsproductos/eone-1602a1.pdf (pdf).
It says that the minimum input voltage for a logical high is 2.2V so if it powers up on 3.3V it may work with the Pi.
Otherwise you would have to connect it to 5V and make sure the display's output pin voltages are dropped to 3.3V using a voltage divider as in the image below. Here the LCD's pin is connected to one of the Pi's ground pins through two resisters and the pin on the Pi that you choose to read input from the LCD is connected between the two resistors.
As suggested here on Sparkfun.
You would need to have a separate divider for each Data pin.
The Raspberry Pi assumes a voltage input of > 1.3V is a logical high so you can use different combinations of resistors if you don't have the exact ones (3.3K Ohm, 1.7K Ohm) so long as the Pi sees a voltage in the range 1.3-3.3