The crew were in waters off Campbeltown Loch, near the Kintyre peninsula, when they issued a mayday call for immediate assistance early yesterday morning.
The Campbeltown RNLI lifeboat was launched and the Campbeltown Coastguard Rescue Team was sent to the scene. A Royal Navy rescue helicopter from Prestwick was also scrambled.
The boat was said to be the Argent, which is registered in the village of Portavogie, in County Down, Northern Ireland.
Rescuers found the vessel wedged on rocks, which had damaged its hull, allowing seawater to pour in.
Four crew members were taken to shore by the lifeboat at 2.30am, where three of them were arrested by police for breaching safety laws.
Gary Young, watch manager at Belfast Coastguard, said: "Campbeltown lifeboat was quick to arrive on scene and safely transferred all four fishermen from their stricken vessel, with no reported injuries."
Later, a spokeswoman for Belfast Coastguard said: "The crew were breathalysed, arrested and charged by police in Campbeltown."
A spokeswoman for Strathclyde Police said: "Three men were arrested, aged 38, 46 and 53, in connection with alleged offences under the Railways and Transport Safety Act 2003."
The boat is thought to have been fishing in the area when it ran aground on the rocks, which lie just off Campbeltown harbour.
Concerns have been raised over the amount of fuel on board and the possibility of it leaking into surrounding waters.
The lifeboat service mounted an operation to ensure any pollution was contained.
A spokesman for the Campbeltown lifeboat station said last night: "We were out for most of the day putting control measures in place. There's between 500 and 1000 gallons of fuel on board.
"It's not leaking at the moment, but there is bad weather on the way, which could affect the position of the boat on the rocks.
"We did not get the fuel off the boat, but it is a very difficult job. The harbour authority will now take over and make an assessment on what to do next."
The spokesman added he could not comment on the arrests, but said the men were not local.
Pollution booms have been put in place and the harbour authority officials plan to return today to try to remove the remaining fuel.