Yes. A US citizen or LPR father can petition for his son even after the son was deported. However, whether the son will be able to get a visa from the US consulate to come back or not will depend on the particular circumstances of his case. He should consult with an immigration attorney before taking any action.
Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. Since we do not have all the facts, it is impossible to give a completely accurate answers. Why was he deported? Does he have any criminal history? Was he granted "Voluntary Departure" or was there an order or removal/deportation. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your son's situation. (S)he would then be in a better position to analyze his case and advise you of your options.
A consultation with an attorney is needed. To sponsor son for permanent residence, a waiver might be required depending on the basis for deportation. Also, the priority date for the family petition must be current.
More information is needed. Although a petition can be filed and perhaps approved, it is unclear whether the petition will be revoked where he is permanently inadmissible as an aggravated felon for immigration purposes. In addition, he needed to register his arrival at the the U. S. Consulate or Embassy. If not, then it may be difficult to confirm that he left the U. S. when he claims that he left. I strongly recommend an appointment with a competent and experienced immigration attorney before further complications and frustration emerge. Good luck.
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