I believe you can do it in many different computational chemistry software, but I use Avogadro most of the time. Just draw your molecule (or open your output file, xyz file, etc.), click on view > properties > bond properties and a list will open, showing all rotatable bonds. But if you want to do it for a big molecule, like a protein or something like that, it might not be the best software, since it does not tell you the number of rotatable bonds, it only shows a list, which is just fine for small molecules, since you can simply count it.
You can certainly do it with the Chemdraw plugin for Excel. I expect the function is somewhere in Chemdraw proper, too. As for free software, I'm pretty sure LICSS (available as an Excel plugin) will calculate that parameter, though you would have to provide input as smiles strings.