I DON'T HAVE TIME IS USED MORE OFTEN...IF YOU SAY I HAVE NO TIME SEEMS A SORT OF IMPERATIVE..YOU CAN USE IT ALONE..AND THE FIRST IN A SENTENCE

Informal - no time -

"I don't have any time" can be use as well.

both are correct. but "I have no time!" sounds much more categorical

"I don't have time" is used more often.