Can a felon be president?
Yes.
There's nothing in the Constitution that says a president can't be a felon.
List of American federal politicians convicted of crimes
https://en.wikipedia.org/wiki/List_of_American_federal_politicians_convicted_of_crimes
This list consists of American politicians convicted of crimes either committed or prosecuted while holding office in the federal government.The politicians are sublisted under the President they served. It includes politicians who were convicted or pleaded guilty in a court of law; and does not include politicians involved in unprosecuted scandals (which may or may not have been illegal in nature), or politicians who have only been arrested or indicted. The list also does not include crimes that occur outside the politician's tenure unless they specifically stem from acts while they were in office. It does not include convictions which were vacated (e.g. Ted Stevens (R)).
Although the convicted politicians are arranged by presidential terms starting with the most recent, many of the crimes have little or no connection to who is president. Since the passage of 20th Amendment on January 23, 1933, presidential terms have begun on January 20 of the year following the presidential election; prior to that, they began on March 4.