Making an object rotate around itself while moving around.

I'm currently working on a game that involves swimming. When the player isn't pressing anything, the character is in a neutral resting/floating position (the character is floating upright). When I press the W (forward) button, the character starts to swim. I'm trying to figure out how to make the character perform a slerp rotation to rotate 90 degrees around its x axis so they become horizontal (swimming forward).

How would you go about making a character rotate only 90 degrees (with a slerp) from an upright position independent of which direction they're facing? I would prefer to use Rigidbody.MoveRotation (since my other code uses that function - this is for a platformer game).