It is not contain C-H covenant bond structure so it is not organic compound structure of ammonium cyanate is [NH4]+[NCO]-
it is inorganic salt and polar compound because of opposite charge ion. see the attachment for structure.  
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Organic compounds mainly contain C-H bonds and one or more of them.
 They also contain  C-C bonds, single or double.

Ammonium cyanate contains bbonds among Nitrogen and Hydrogen.  Cyanate contains among Nitrogen and oxygen.
It is an inorganic compound.  Ionic.
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