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我是美国公民， 16岁的儿子是加拿大公民， 他跟我前妻住在加拿大温哥华， 前妻拥有全部监护权。 请问我可以给儿子申请美国绿卡或公民吗？

-Yes, you can file I-130 to sponsor your kid to apply for immigrant visa (green card) in Canada, but you have to have the physical custody right.  Otherwise, if your ex-wife does not agree, your son will not get the immigrant visa unless your son is > 18 years old later.

After your son get the immigrant visa to enter US, then he will automatically become a US citizen if he is less than 18 years old at that time.