I bought Movie Studio 12 on disc for my old Del laptop. But I've recently gotten a Mac Pro and since it doesn't have a disc drive, I can't reinstall it.
Are there any other ways I can reinstall it?
There are two ways that you can run Movie Studio on your Mac:
One is to run Movie Studio in a virtual machine on your Mac. I use VMware Fusion to do this ($79.99) but you can also use Parallels Desktop or download the free VirtualBox and create a Windows virtual machine and install Movie Studio into that by downloading the latest update from Sony's web site and activating it with your license key. No need for a DVD drive.
Here is Vegas Pro running in VMWare Fusion on my MacBook Pro desktop in Unity mode so that it interacts with other windows on my Mac desktop:
The second is to use Bootcamp which allows you to install Windows on a separate partition on your Mac SSD and boot into it just like a normal Windows PC. That that point, you can install any software you want that requires Windows. This method fully supports GPU acceleration and since Apple uses AMD GPU's for the Mac Pro, it makes an excellent workstation for running Movie Studio and Vegas Pro. (BTW, I have a 2010 Mac Pro 12-Core w/ 24GB memory and an AMD Radeon HD 7950 GPU and it runs Vegas Pro great!)
The easiest thing to try is the first method using VirtualBox, Parallels Desktop or VMware Fusion. The only thing you loose with this method is GPU support. If you need to use GPU acceleration then you must use Bootcamp.