You will most likely be able to marry him. Just figure out what the marriage laws are where you live.
But the more difficult part will be trying to help your boyfriend obtain legal status in the United States. If he has been deported before, and if he has entered the United States again illegally, then he might have a very difficult time obtaining legal status at this time.
More information is required to determine what might be possible for him regarding his immigration status. I suggest that your boyfriend consult with an experienced immigration attorney near you and review all of his immigration history, as well as any encounters with law enforcement.
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I am assuming you are a US citizen. If he has been deported in the past and has reentered the US without inspection, its going to extremely difficult to legalize his status in the US, even if you do get married. You need to consult with an experienced immigration attorney at the earliest.
Marriage may not help him for another ten years. His prior order can be reinstated at any time.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
You can marry anyone you want. Whether or not your boyfriend/fiance can obtain status is another issue. Based on his history it will be difficult and you will need counsel.