The wilful fireraising happened just before midnight at Greenlaw Dean on Tuesday, June 8.
Police Scotland said that a large quantity of plastic crop cover rolls were deliberately set alight.
There were no injuries, however the fire could easily have spread.
Officers are keen to trace the occupants of two vehicles seen in the area at the time.
Detective Liam Myers said: “This was a reckless and dangerous act and we're carrying out enquiries in the local area.
"We’re appealing to anyone with information on the fire which could assist our enquiries to please come forward.
"We're also looking to hear from anyone who was in the area and may have seen anyone suspicious around the time of the incident or anyone in Greenlaw who has CCTV.
"We are particularly interested in two silver or white BMW / Audi type saloons which were seen in the area at the time."
Anyone with information is asked to call police on 101, quoting incident 0055 of June 9. Alternatively, contact Crimestoppers on 0800 555 111, if you wish to remain anonymous.