As far as I can see it's not a direct quote; I only found examples of indirect speech.
In LOS POETAS Y SU VOZ - 3 Federico García Lorca, Gabriel Celaya, Gerardo Diego, the "quote" goes as follows:
En esos momentos políticos alguien le preguntó sobre su preferencia política y él manifestó que se sentía a su vez católico, comunista, anarquista, libertario, tradicionalista y monárquico.
Translation:
In those political moments, someone asked him about his political preference and he stated that he felt in turn Catholic, communist, anarchist, libertarian, traditionalist and monarchist.
The text goes on to say that for this reason, he never joined a political faction and never distanced himself from any of his friends for any political reason.
The "quote" can be found on several other websites, e.g. in the article Federico García Lorca: “En la bandera de la Libertad bordé el amor más grande de mi vida.” on La Política, on the website Granada por el Mundo, in the article El 18 de agosto de 1936 falleció Federico García Lorca, es el poeta de mayor influencia de la literatura española del siglo XX on Universia and on many, many blogs.
You can find the statement also on the Spanish Wikipedia, which cites a source that uses a slightly different formulation (my emphasis):
Antes de ser asesinado, el poeta fue interrogado sobre sus preferencias políticas. Lorca, que nunca estuvo afiliado a ninguna fuerza política, manifestó sentirse al mismo tiempo "católico, comunista, anarquista, libertario, tradicionalista y monárquico".
English translation:
Before his assassination, the poet was asked about his political preferences. Loca, who never affiliated with any political force, said that he felt at the same time "Catholic, communist, anarchist, libertarian, traditionalist and monarchist."