Are there any popular melody or tune to sing a haiku poem?
No single melody can properly fit all English haiku, because each poem stresses different syllables. This may also be true for 5-7-5 haiku in other Western languages. Furthermore, some scholars argue that 5-7-5 poorly translates the Japanese concept, and that other syllable counts are justifiable. In that case, even the number of syllables is not known. The only possible melody would be something like a Psalm tone.
Similarly, in Japanese poems, the lengths of mora may differ. The quality of word underlay in Japanese surely depends as much on mora lengths as it does in English on scansion.
Perhaps each haiku may need a slightly different melody. For a non-serious haiku, try a 12-bar blues. Or maybe a Folia (using the 9-bar version).
None of these short poetic forms seems too easy to set. Omar Khayyam's stuff isn't easy either.