How do you calculate or predict the charge of a protein at pH 7?
ExPASy to the rescue! Although I didn't comb through all the tools, this nifty website provides quite the myriad of bioinformatics resources which most certainly contains the tool to calculate what you want.

Bear in mind though, most tools will tell you the isoelectric point of your protein. However, bearing in mind the relationship between pI and pH (i.e. if pI &lt; pH, then protein is - charged, and vice versa), you can easily figure out the charge of a protein at pH 7.

http://expasy.org/tools/

*Update

Here's the exact tool to calculate isoelectric points: http://web.expasy.org/compute_pi/