Look it up and you'll _realize_ that "realise" is the non-Oxford English spelling, and the Oxford English spelling is realize.
It's the same with many words with the -ize suffix - we seem to have subconsciously accepted -ise to the point that spellcheckers demand it, when in actual fact the OED form of a word typically uses -ize.
Most British newspapers use the -ise form. The Oxford University Press use the -ize form. So it isn't as clear cut as you think.
I recall reading that the -ise alternatives have some roots in Australian us of the language.