This is supposedly one of those things where "
disc" is the
British spelling and "
disk" is the
American spelling. Most computer things come out of the US these days, so we get used to seeing "
program" and "
dialog" in computer contexts.
Philips, inventors of the
CD, are a
Dutch company, so they used the British spelling, and as they got to copyright the technology everyone has to follow them for Compact Disc.
But this is not a normal British/American difference. The only other comparable pair is mollusc/mollusk. I only know two other words ending in -sc, and they're pretty obscure: subfusc and fisc. I'm not sure whether they're written subfusk and fisk in American.
The odd thing is, -sk is the natural English ending: mask, task, flask, desk, risk, tusk, musk, tusk. The C/K sound is almost always written K after another consonant: park, lurk, talk, folk, ink, bank...
The older form of the word in English would be disk rather than disc: but what it actually becomes in Old English is dish, and in Middle English it's desk and dais.
The Greek diskos meant a small round thing for throwing, a discus or quoit. It was borrowed into Latin as discus, but later came to mean a small round table. This is how it comes to be borrowed into Old English as dish, then into Middle English as desk (via the Italian form) and dais (via the French form). The dais was originally the table itself, then later the platform it stood on.
So it's the "British" spelling disc that's slightly odd - we wouldn't expect it to line up with Latinate technical terms like mollusc, subfusc, fisc; why isn't it an ordinary K word like risk, desk?