According to this it has a SATA connector - but in you second picture only the lower connector looks like one. This is the same model from a Macbook:
View attachment 1919988
on the right you see the black SATA connections. If your connector on the drive looks similar, you can use a SATA-to-USB adapter, there are plenty (with and without case).
"The DVD drive use slimline SATA connector. OP would need a 22pin to 13 pin adapter/cable + SATA to USB adapter, or the exact USB enclosure for laptop DVD drive."
By the time the OP buys all this stuff, it might have been cheaper to buy a brand-new external USB DVD/CD drive...