Yes. In fact it has happened several times. In 1884 Mexico and the US agreed to create The International Boundary and Water Commission to manage precisely these changes. From time to time additional treaties have been drawn up and commissions formed to sort it out. Some of the bigger ones have been:

1933 - The Rio Grande Rectification Project saw the transfer of 174 parcels of land back and forth, and the main channel was deepened and straightened in places.

1963 - The Chamizal Convention resolved a long standing dispute over the Chamizal, after the river moved. A new border was agreed on, and a new channel was constructed to mark the new border. This didn't match either the old channel or the existing channel.

1970 - The Boundary Treaty reestablished the concept of a moving border to follow river changes. It also included a number of small land swaps to account for some proposed flood control projects.

There have been more recent ones as well. All of these have involved a few square miles of land total.