If I play Harrowing and bring Annie back into play, can Annie's ability target the Harrowing that was just played to get it back?

Ruling: Yes, you can get The Harrowing back with Annie's ability. Spells enter the trash as the final step before being considered fully resolved/played, which happens before Annie finalizes and her trigger goes on the chain.

Sequence:

• You play The Harrowing targeting Annie in the trash
• Reactions may happen, The Harrowing begins resolving
• Annie is placed onto the chain as pending (will finalize during next cleanup)
• The Harrowing goes to the trash and is now considered Resolved/Played
• This causes a cleanup, Annie finalizes to the chain
• Since she is a permanent, she resolves immediately and her trigger is added to the chain
• The Harrowing is in the trash at this moment, so it is a legal target for Annie's ability