Q:

Are there any words which use 'カ', the on-yomi of 何?

I started finally learning kanji's readings not only meanings and words. And in two sources I use I see that 何's kun'yomi is なん、なに and on' is カ.
I've seen 何 in many words as
なん: 何度、何と、何で
なに: 何人、何か
ど: 何処、何の
何れ (いずれ)、何時(いつ)

I know, that ど and い readings can be exceptions.

But never as カ. Are there any words that is it as カ?

A:

You are correct that there are many more common uses of the 訓読み なに or なん for 何 when compared with the words which use the 音読み カ.
But here is one example: The word for 'geometry' is: 

幾何学 (きかがく) - definition

Although it also seems to appear in words like 如何せん (いかんせん) or 如何 (いかが), I don't think those are strictly standard usages of the readings but more of a jukujikun type (reading by meaning). For example, い is not a standard reading of the kanji 如 (see here for details). Therefore I'm not sure that 如何 qualifies as a usage of the 音読み here.   
There are probably more examples - I will check and edit in others if I find them.

