Noticed that there wasn't an answer for this question so I am going to provide something simple that will work at any FPS as you suggested:
You could do something simple involving what angle you want to move to, that being 90°, and the duration you want to complete that movement in.
Taking the your designated time, say it's 3 seconds, you can convert that to frames using the given delta with
Gdx.graphics.getDeltaTime() or the given delta in the render loop:
frameTime = timeInSeconds * (1 / Gdx.graphics.getDeltaTime());
// 3 * (60) = 120 ( which is how many frames over 3 seconds if your running at 60 fps)
Note, the getDeltaTime() and delta variable are 1 / fps, so you need to get the inverse of the delta to get the fps.
Then you can take your designated rotation amount, 90°, and find the amount it needs to rotate every frame:
degreesEveryLoop = 90 / frameTime;
// 90 / 120 = .75 (So if you wanted the player to move 90° over 3 seconds then you would need to move .75° every frame
Then you would just need to apply the amount to the player every frame