Yes, you can calculate the radius of gyration by Gromacs by using g_gyrate command. You can also install Gromacs on windows but for that first you will have to make the UNIX environment in Windows by following the above-mentioned link by Justin. And it also faces the crash problem in Windows as Gromacs needs the high server capability and stable OS. I would rather prefer Linux.
If you face the problem in installing it in Windows as well as in Linux, you may simply install in Ubuntu 10.04 LTS version through the synaptic package manager which installs the Gromacs without any trouble.
After the execution of the command you will be prompted for a selection of the part of your trajectory that you want to analyze. I normally used option (5) - mainchain.