I assume you mean "is exiled rather than sacrificed" rather than just "is exiled".
That's a decision for whoever controls the permanent that would go to the graveyard. Here, there are two replacement effects that would affect where the permanent would go, so that permanent's controller chooses which effect to apply (C.R. 616.1). Thus, for example, if the permanent that would go to the graveyard is controlled—
by your opponent, they can choose to apply the Samurai of the Pale Curtain they control so that they exile the permanent instead, rather than you; if they exile the permanent this way, Ranar's last ability won't trigger for that permanent.
by you, you can choose to apply the Samurai of the Pale Curtain you control so that you exile the permanent and so satisfy Ranar's last ability.
by a player other than you or your opponent, that player chooses which replacement effect to apply (and so decide who exiles the permanent in this case).
Note that Samurai of the Pale Curtain's second ability applies to any permanent (not just lands like Windswept Heath) that would go to any graveyard by any means (not just by sacrificing). It doesn't apply if a permanent would be exiled directly (such as by Swords to Plowshares or Banishing Light).
With the release of Strixhaven: School of Mages, the Oracle text of Ranar changed in a manner that materially affects this question.
Specifically, on Ranar's last ability, the text "Whenever you exile..." was changed to "Whenever a spell or ability you control exiles...".
However, this text change made the behavior of Ranar unclear in the face of replacement effects that exile permanents, such as with Samurai of the Pale Curtain. This is especially since at the time of this writing, the only abilities that the comprehensive rules speak of as having a controller are activated and triggered abilities on the stack (C.R. 113.8; see also C.R. 109.4), not static abilities such as Samurai of the Pale Curtain's second ability (C.R. 113.3d; compare C.R. 113.1c with C.R. 113.1).
And unfortunately, the update bulletin for Strixhaven: School of Mages didn't point out this Oracle text change in Ranar, and neither did the update to the rules add clarification on whether foretell (C.R. 702.142a), Samurai of the Pale Curtain's second ability, or other static abilities have controllers for purposes of Ranar's triggered ability. (Indeed, the bulletin went over Elemental Expressionist, where "When you exile this creature..." was changed to "When this creature is put into exile...", although for different reasons than the case of Ranar.)