Can I travel across the border if I am charged with drug possesion?

Yes.  You may travel while your drug charges are before the courts.  Remember, you are presumed to be innocent at all times.  However, border guards/homeland security personel have very broad powers to deny anyone access to the country.  It is unclear what is shared with U.S. and international authorities and the timing of any sharing that occurs.  Some of my clients sail through without difficulty and others experience delay.  Travel to the United States and some other countries like Mexico, Cuba and England may prove to be more difficult than other countries.  My advice is to try a day trip across the U.S. boarder on a day when you do not have a time deadline.  Purchase something in the United States and declare it on your way back.  This way, you will be typed into the system and you will know whether you have been flagged in any negative way.