Yes, surprisingly,
The Moirai were independent, at the helm of necessity, directed fate, and watched that the fate assigned to every being by eternal laws might take its course without obstruction; and Zeus, as well as the other gods and man, had to submit to them.
From here
Quintus Smyrnaeus,
"To the Moirai (Moirae, Fates) the might of Zeus must bow; and by the Immortals' purpose all these things had come to pass, or by the Moirai's ordinance."
We see this directly in a known myth,
Nonnus, Dionysiaca,
"[Zeus swore he would grant Semele a wish, but she requested he appear before her in his full glory which would bring her destruction :] Father Zeus heard, and blamed the jealous Moirai (Moirae, Fates), and pitied Semele so soon to die . . . [Zeus tried to dissuade her] but he had no thought of fighting against the threads of Fate."
But Zeus was the guide...
Pausanias, Description of Greece
"[In the temple of Zeus at Megara :] Above the head of Zeus are the Horai (Horae, Seasons) and Moirai (Moirae, Fates), and all may see that he is the only god obeyed by Moira (Destiny)."
Pausanias, Description of Greece
"[In the shrine of Despoine (Despoena) at Akakesion (Acacesium) in Arkadia :] On the first relief are wrought Moirai (Moirae) and Zeus surnamed Moiragetes (Guide of Fate)."
Zeus was the Moiragetes- the Guide.