Yes, you can, if you know the right formula for the right species of cricket. Amos Dolbear developed an equasion, called Dolbear's law, for finding temperature from the chirps of the Snowy Tree Cricket, (Oecanthus fultoni). Fortunately, the same formula works almost as well for the Common Field Cricket shown here. To calculate it:

Take the number of chirps in one minute.
Subtract 40.
Divide by 4.
Add 50.

That will give you the temperature in degrees Fahrenheit.