Download stats.ny from [u]this post[/u] and copy it to your Plug-Ins folder. Then open Audacity, load your file and go to Analyze → Wave Stats. You can use RMS or A-Weighted RMS levels. You may also want to check the peak levels, since noise generally has a lot of randomness.
You can’t get actual dB SPL readings unless you calibrate your setup with an SPL meter, but the relative readings will be valid as long as you don’t change anything in your recording setup. i.e. A 6dB drop in your digital (dBFS) reading means a 6dB drop in your acoustic (dBSPL) level.