It depends what you mean by this. If you mean did pirates like Blackbeard and Bartholomew Roberts in the “Golden Age of Piracy” in the early 18th get individual merchants to pay them protection money in order to not attack that specific merchant’s ships on the high seas, the answer to that is no. That would have been completely impractical for a number of reasons.

Firstly, pirates were very disorganized and didn’t usually cooperate with each other except opportunistically, so if one pirate crew made an agreement with a particular merchant, that wouldn’t be abided to by any other pirate. Secondly and most importantly, in order to operate a protection racket, the racketeer usually needs to be a serious and specific threat in a specific area, but the sea is a huge place and pirates often sailed huge distances and weren’t in one place for long. Merchants wouldn’t have any incentive to make special deals with pirates, both because the likelihood of one of their ships getting captured by pirates was extremely low and because a deal with one pirate means nothing to all the rest. The pirates also wouldn’t have any incentive to avoid attacking certain merchant ships when they could just get away with all the money by robbing them completely. When pirates captured a merchant ship on the open ocean the interaction wasn’t anything like the Mafia going into a local business and getting them to pay some money every month to not get their windows broken. It was basically the equivalent of a single random mugger stealing someone’s wallet in a dark alley: the pirates would never see their victim again and vice versa.

That said, there were other ways that pirates and buccaneers engaged in protection rackets of sorts, especially in earlier periods before the stereotypical “Golden Age of Piracy.” In the 17th century, buccaneers very often bribed local governors in the Caribbean and elsewhere to either turn a blind eye to their piracy or outright support it by granting them legal privateering commissions or letters of marque which authorized them to attack enemy ships and settlements during times of war. In return, the buccaneers would not only in theory have government backing but also a port at which to spend their loot and recruit new expeditions. This was a bit like racketeering but on a national level, i.e. “You give us support and we’ll leave your country’s ships alone and only attack the country you’re at war with.” It was also a mutually symbiotic relationship where basically everyone benefitted except for the enemy nation being robbed and plundered: the governor would receive bribes and payments, the buccaneers would get a friendly port to use, and the local businesses would get lots of drunk pirates who were very eager to frivolously spend their stolen loot. This is what was happening in the famous “pirate havens” like Tortuga and Petit-Goâve and Port Royal and later Nassau.

When official wars ended, these privateering commissions that were legally issued by local governors were supposed to become invalid. However, because of bribes and other benefits, corrupt governors would often still condone and give shelter to buccaneers while they continued preying on foreign ships in acts of outright piracy despite no official hostility existing between the respective nations. Even Blackbeard did this briefly when he bribed Charles Eden in 1718, the governor of Chares Town in South Carolina. To make a more modern analogy, this would be very similar to gangsters paying off local police chiefs and officials to turn a blind eye to their crimes. Essentially the pirates were paying protection money to the authorities in this case.

Another racketeering of sorts that buccaneers engaged in was ransom. When they captured a usually Spanish town, they would almost always hold it for ransom. They would of course loot all the valuables they could find and torture their prisoners into revealing hidden valuables to begin with, but then if the Spanish refused to pay a further ransom that was demanded, they would completely demolish the entire town and burn it to the ground. They would also hold their prisoners for ransom and if the Spanish refused to pay the ransom to free them, the buccaneers would either execute them or transport them off to use as slave labor or rot in some prison. That’s obviously extortion and technically a form of racketeering.

One illustrative example of how these dynamics worked can be seen after the Treaty of Madrid in 1670, which was a peace treaty between England and Spain which ended a long period of hostilities. The English governor of Jamaica at the time was Thomas Modyford and under his protection, English and French buccaneers in the Caribbean had for the previous fifteen years made Port Royal their base of operations where they spent their loot and recruited new expeditions against the Spanish. When peace was declared with Spain in 1670, the most powerful buccaneer Henry Morgan was already planning another attack against the Spanish, and with the aid of Thomas Lynch he simply ignored the treaty and plundered the Spanish city of Panama anyway in January 1671. Henry Morgan knew his career as a buccaneer was over after that point, so after plundering the city he sailed away without dividing up most of the loot, leaving most of the 2,000 buccaneers behind. Probably because of this, although Henry Morgan and Thomas Modyford were both subsequently arrested and taken back to England, they were soon released and Henry Morgan was even knighted by Charles II and appointed the new governor of Jamaica. We can imagine he probably bribed a lot of important people with the Spanish treasure he had embezzled. In a sense, Henry Morgan was basically paying protection money to the English government. The Spanish were obviously very enraged by this, but they couldn't afford to go to war with England so they had to accept England's flimsy excuses that Henry Morgan somehow didn't know about the Treaty of Madrid even though there is definitive proof that he did.

As for the cheated buccaneers that Henry Morgan left behind, many of them afterwards turned to the French governors of Tortuga and Petit-Goâve for employment, who unlike the English were still willing to condone their attacks against the Spanish by selling semi-legal privateering commissions to at least give a veneer of legitimacy to their plundering. This continued until the 1680s when the French -- like the English before them -- also began cracking down on the buccaneers because they seriously jeopardized peaceful trading relations (as exemplified by cases like Henry Morgan). In 1684, the French governor Tarin de Cussy offered pardons to buccaneers who agreed to hunt down their rogue former allies who continued attacking foreign ships without valid commissions. By the 1690s the classic era of buccaneering was gone but from 1702 until 1713, England, France and Spain once again (but for the last time) employed large numbers of privateers against each other during the Spanish War of Succession. When hostilities ended with the Treaty of Utrecht, the privateers characteristically refused to stop plundering, but unlike before, no other European government was any longer willing to give them a safe haven. Previously, governments might have felt compelled to employ these restless privateers lest they defect to their enemies to use against them in the next war (as many English buccaneers had gone over to the French after 1670), but things had changed and there was no longer any European nation willing to do so. To once again give a modern analogy, this might be equivalent to a massive police reform to crack down on crime and police corruption. In response to this zero tolerance policy toward pirates, the remaining pirates who weren’t cowed into surrendering adopted their own no tolerance policy and for the first time began indiscriminately attacking all ships with no regard whatsoever for nationality since they no longer had any pretense of being legal privateers. These pirates continued to control the island of Nassau in the Bahamas for a few years, but this was easily taken over by the British navy in 1718 and within ten years virtually all Western piracy had been eradicated. I made another post about how piracy ended here.

Sources and further reading:

The Buccaneer's Realm: Pirate life on the Spanish main, 1674-1688 by Benerson Little

The Sack of Panama: Captain Morgan and the Battle for the Caribbean by Peter Earle

The Republic of Pirates by Colin Woodard

Under the Black Flag by David Cordingly