Rankin, 49, found the blazing bins in his street in the Merchiston area of Edinburgh on Wednesday morning.
Police have described the act as “mindless vandalism” and are appealing for witnesses.
But Rankin – whose Rebus detective novels have made him a household name – has decided to put his own crime fighting skills to the test.
In a tongue in cheek tweet following the incident Rankin said he was looking for someone with “v long legs” because of the gaps between burnt bins.
He also warns the vandals “we will hunt you”.
Rankin said: “I deduce that some form of accelerant must have been used. And since only every third or fourth bin was torched miscreant must have had v long legs.”
Famous for crime and writing, Rankin goes on to gaffe, with a spelling error in one of his tweets.
He said: “To the evil doers who torched several wheelie bins in my street – you cannot win. Our resole is strong.”
Rankin adds: “I meant resolve, obviously.”
But he leaves the “evil doers” in no doubt as to his intentions. He said: “We will hunt you down…”
Police said they were appealing for witnesses for the incident which happened on Wednesday morning between 3am and 3.30am.
Officers said that bins which had been left for collection had been set alight on Napier Road and Polwarth Terrace.
Nobody was hurt in the incident and no damage was caused to houses.
A spokesman for Lothian and Borders Police added: “Fortunately no one was injured, but this mindless act of vandalism could have had serious consequences.
“We would appeal for anyone who was in the area at the time, and who might have seen something suspicious, to contact police.”
Rankin confirms that officers had been to see him regarding the incident in another jokey tweet.
He said: “Filth at door this afternoon; flushed the drugs ‘n’ buried the gun in compost heap, then remembered: they were here re wheelie-bin fires..”