Cuba’s new migration rules throw the ball back into the U.S. court on travel between the two countries, and analysts say it could turn U.S. migration policy for Cubans on its head.

“It could put the United States in quite a pickle,’’ said David Abraham, professor of immigration law at the University of Miami.

But that won’t be because of a sudden influx of Cuban travelers arriving in the United States on charter flights. While Cubans may flood the U.S. Interests Section in Havana with requests to visit the United States, the U.S. State Department said Tuesday that visa requirements for Cubans remain unchanged.

Cuba announced Tuesday that on Jan. 14, it will eliminate letters of invitation and the so-called tarjeta blanca, or exit visa, which Cubans have needed to embark on foreign trips.

“I don’t see the United States greatly expanding visas, but something is going to happen,’’ said Bob Guild, vice president of Marazul Charters, which offers service between Miami and Havana and Camaguey.

That change? Analysts said that when it becomes easier for Cubans to leave the island, the number traveling to third countries such as Mexico or Canada, and then using them as a springboard to enter the United States could increase.

In the first nine months of this fiscal year, for example, 7,401 Cubans entered the United States through the border with Mexico.

Under the Cuban Adjustment Act and the United States’ wet-foot, dry-foot policy, Cubans who present themselves at the border can be paroled into the United States and then become permanent residents a year later. Because they have arrived by land (dry foot), they are allowed to stay. Had they been intercepted at sea, they would be sent back to Cuba.

There are also other circuitous routes that Cubans are using to enter the United States and take advantage of the Cuban Adjustment Act, and analysts say such traffic might increase.

Ecuadorean President Rafael Correa, for example, eliminated entrance visa requirements for Cubans in 2008. Already, smugglers are taking Cubans who enter Ecuador across Colombia to the rugged Darien Gap between Colombia and Panama and then on up to the Mexican border.

Some Cubans also are taking advantage of Spain’s Law of Historical Memory, which granted Spanish citizenship to children and grandchildren of Spaniards who left during the Spanish Civil War in the 1930s and the ensuing Franco dictatorship.

With a Spanish passport, Cubans can travel to a neighboring island then use the passports to travel to the United States. The U.S. doesn’t require visas from Spanish visitors.

The U.S. government said it plans to monitor possible changes in migration patterns from Cuba caused by the new migration rules — which could prompt its own response.

“The United States welcomes any reforms that will allow Cubans to depart from and return to their country freely,’’ the State Department said.

A spokesman said the United States remains committed to 1994 migration accords between the two countries that support orderly and safe migration. Under that agreement, the United States promised to admit not less than 20,000 Cuban immigrants annually, not including immediate family members of U.S. citizens.

In addition, the United States issued 17,848 non-immigrant visas in fiscal 2011 and 2,223 visas for travel by immediate relatives.

“Cuba is telling the United States to put its money where its mouth is. It has said it wants free travel, and the Cubans are saying, ‘Well, here it is,’ ’’ said UM’s Abraham.

Meanwhile, none of several air charter companies contacted by The Miami Herald said they’re expecting much of an uptick in business — unless the United States changes its visa policy.

“I don’t think it will make much difference,’’ said Vivian Mannerud, president and founder of Airline Brokers, a charter company that operates six flights weekly from Miami and Fort Lauderdale to Cienfuegos and Havana.

“Now, the exit visa won’t be the hard part,’’ said Mannerud. “The entrance visa will be the hard part.’’