Some airlines apparently provide an option for passengers to purchase carbon offsets:

See:
https://www.united.com/web/en-US/content/company/globalcitizenship/environment/carbon-offset-program.aspx

But there is no assurance of their validity, and when this "first got off the ground" the prices were unbelievably low, leading some to conclude it was just a PR scam.

See:
http://mobile.nytimes.com/2009/11/18/science/earth/18offset.html