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我是美國公民， 16歲的兒子是加拿大公民， 他跟我前妻住在加拿大溫哥華， 前妻擁有全部監護權。 請問我可以給兒子申請美國綠卡或公民嗎？

-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.