Presently it is affiliated with the Anglican Church of Canada.
From here:
Members of synod for the Episcopal Church of Cuba narrowly voted in favour of returning to the church’s former affiliation with The Episcopal Church at their recent meeting last month in Cardenas, Cuba.
The move came two months after the historic decision by the United States and Cuba to re-establish diplomatic relations after a 54-year hiatus. The Cuban church had been part of a province in The Episcopal Church until the 1959 revolution, which made travel and communication between the two churches difficult. The Metropolitan Council of Cuba (MCC)—which includes primates of the Anglican Church of Canada, the Province of West Indies and The Episcopal Church—was subsequently created to provide support and oversight.
Archbishop Fred Hiltz, primate of the Anglican Church of Canada, and Archdeacon Michael Thompson, general secretary, attended the synod—which ran from Feb. 19 to 22—as representatives of the MCC.
This will mean a big change for Cuban Anglicans: they will move from a Province that is radically liberal, blesses same-sex unions, boasts practising gay clergy, believes dogma is redundant, and is losing people faster than Obama is losing votes to a Province that that is radically liberal, blesses same-sex unions, boasts practising gay clergy, believes dogma is redundant, and is losing people faster than Obama is losing votes.
The decision was made, it seems, largely so Cuban clergy could retrieve their pension funds, proving that, no matter how vehemently they may protest otherwise, when it comes to their livelihood, Cuban clergy are just like their North American brothers: capitalist running dogs:
Hiltz went on to explain that one of the significant factors behind the drafting of the substitute resolution is “the frustration of a number of people in the church in Cuba with the fact that since the break with The Episcopal Church and the political situation between Cuba and U.S., the pension fund for clergy has just basically been frozen [in the U.S.].”