When you installed a game for the first time (from the disc version), you had to put the cd-key or serial included with your disc.
At that moment of inserting the cd-key, the game was added to your Origin library. After that, You don't need the disk anymore. The game is stored in your Origin library & you can download it from Origin any time.
If you still want to install from the disc version, you have two options:
- attach external USB disc reader to the new pc;
 
- make ISO file on the old computer (which has disc reader), copy the ISO file to the new computer, and install the game from the ISO file (emulated* disc drive);
 
- (Be aware, that after installing from the disk version there will still be massive patching/downloading!)
 
*Note: Windows 10 already has virtual ISO disk drive supported, but if you want you can install eg. Virtual CloneDrive or DAEMON Tools... see the following link:
https://www.geckoandfly.com/18377/5-best-iso-mounting-free-software-for-creating-virtual-cd-dvd-drive-in-microsoft-windows/