The 29-year-old, who is set to start for the Warriors in Sunday's Heineken Cup clash with Leinster, made the remarks about the US president on the social networking website and has been reminded about his future conduct by the Scottish Rugby Union.
A statement from the SRU read: "Social media provides a platform for our players to engage with fans and act as ambassadors for our team and the sport in general.
"We do make players aware of how best to use social media, such as Twitter, so they can make the most of the service.
"We have spoken to Rory about the tweets identified and he fully accepts the language used was completely inappropriate and has apologised unreservedly for offence caused."
Lamont wrote on January 4: "The rise of (Republican presidential hopeful) Ron Paul in the US has to be the most inspiring story in western politics. He doesn't work for wall street like that whore Obama."
Lamont, who is yet to delete the message, said: "If I have ever caused any offence from the language used in my tweets I do apologise."
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