The arrest is the seventh in connection with the incident at the end of September, when five men were arrested in an operation on suspicion of planning a terrorist act.
Another person was arrested shortly afterwards in London.
Those arrested earlier have all been released on bail. But questions remain about the incident, as the US president has claimed it was a terrorist plot and suggested links to Iran.
The US has also moved several aircraft that were stationed at the air base as a security measure.
RAF Fairford has been used by American bombers during decades of conflicts in the Middle East, including this year’s war with Iran.
