From this pic it looks like a regular laptop slimline drive, but to be sure a pic of the interface inside the PC and/or full model name (so we can find the service manual which will list the part number with which we can identify the drive)

The dimensions are probably those of a standard slim laptop, but the interface for the ATA cable may be proprietary—at least that's how it is with the SFF Deskpro EN. It is neither a standard ATA connector nor a floppy connector.

I found a slim cd rom drive with some weird connector that fits this adaptor.
Then I guess I can connect it to the normal IDE port.

Your SFF is newer than the one I posted, and maybe your motherboard only has standard IDE ports—in that case, it would be simple. Look at it first.
But there’s another catch—with a laptop drive, you can’t choose master/slave, so you’re stuck with the manufacturer’s default settings and have to configure the second device on the same cable accordingly, if there is one.