I have Sona on my battlefield. I end my turn. Sona's ability goes on chain and my opponent reacts to it with Star Crossed and sends Sona to my hand. Can I still ready my runes?

Yes — Sona leaving the battlefield in reaction doesn't stop her trigger from resolving.

Her "if I'm at a battlefield" clause is part of the trigger condition, checked when the ability is finalized on the chain (Rule 383.2.a.1), not continuously. Once the trigger is on the chain, removing or killing Sona doesn't stop it, so you still ready up to 4 friendly runes when it resolves (FAQ 2042).

Note her current text is "ready up to 4 friendly runes," so with fewer than 4 runes you just ready as many as you have (FAQ 2277).