How to use Pick Whip to make two objects rotate?

The pick whip needs to be dragged from the property you want to control to the property you want to follow. So:

• Twirl down the text layer's Transform → Rotation property
• Alt-click (Option-click on Mac) the stopwatch next to the text layer's Rotation to enable expressions
• Drag the pick whip from the text layer's Rotation → to the shape layer's Rotation
• The expression box will now show something like thisComp.layer("Shape Layer 1").transform.rotation

Now when the shape layer rotates via keyframes, the text layer follows.
Why your way didn't work
Dragging the pick whip from the shape layer to the text layer would make the shape follow the text — but the text has no keyframes, so nothing happens, and you'd also kill your existing keyframes on the shape (an expression overrides keyframes on the same property).