The typical expressions for "full-time" are:
a/de jornada completa
a/de tiempo completo
Based on the dictionaries I've checked so far, typically one uses the preposition "a" when using the expression as an adverb and one uses the preposition "de" when using the expression as an adjective. Therefore:
a full-time student = "un/una estudiante de jornada completa" or "un/una estudiante de tiempo completo".
For comparison, "part-time" is:
de medio tiempo (adj or adv)
a tiempo parcial (adj or adv)
Some of the dictionaries I've checked say that "de medio tiempo" is used in Latin America and that "a tiempo parcial" is used in Spain.
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