GA Code § 16-5-23 (2017)
- (a) A person commits the offense of simple battery when he or she either:
- (1) Intentionally makes physical contact of an insulting or provoking nature with the person of another;
This offense is not an issue for the US. You were deported because of the overstay and not the offense. You may apply for a green card if you qualify after the exclusion period is completed.
In Canada, the closest offense is assault as Canada does not have a specific definition for battery.
Assault
- 265 (1) A person commits an assault when
- (a) without the consent of another person, he applies force intentionally to that other person, directly or indirectly;
The offense in Georgia is narrower than the equivalent offense in Canada as it requires the contact to be of insulting or provoking nature. This means that, unfortunately, you are criminally inadmissible to Canada at this time. You will have to wait 5 years after your probation period ends to submit a rehabilitation application to enter Canada.
However, since you are or will be married to a Canadian citizen you are eligible to make an application to IRCC on humanitarian and compassionate grounds during this period to overcome your inadmissibility to Canada.