Does Sun Disk Legion tap after playing itself?

No, you cannot play Sun Disc as the first card of your turn and immediately exhaust it to activate its Legion ability.

Clarifying the Requirement

While some legacy FAQ content has caused confusion regarding whether a card counts itself toward its own Legion requirement, official rules clarify that it does not:

• Rule 812.1.c states: "As long as a card different than the one with the Legion ability has been Finalized on the same turn then the Dependent Ability is Active."
• Rule 812.1.b.1 clarifies that Legion is functionally shorthand for: "If you have played another card this turn..."
• FAQ #8715 and FAQ #9616 confirm that Sun Disc does not count as "another card" for its own Legion requirement.

Therefore, you must play at least one other card during the turn before the Legion condition is satisfied and you can successfully exhaust Sun Disc to gain its benefit.

Correct Sequence for Sun Disc

To use Sun Disc successfully, follow this sequence during your Main Phase:

1. Play a different card: Play any other Main Deck card. This satisfies the Legion requirement for the remainder of the turn.
2. Play Sun Disc: If not already in play, you may play Sun Disc.
3. Exhaust Sun Disc: Because you have already finalized "another" card this turn, the Legion ability is active. Exhaust Sun Disc while the game state is "Open."
4. Play your unit: The next unit you play this turn will enter the battlefield ready.

Important Note: If you attempt to exhaust Sun Disc before playing another card, the Legion ability is inactive. According to the rules on dependent keywords, an inactive ability cannot be activated.

Note: I could not fully verify the interaction regarding payment of costs for inactive abilities against the retrieved rules.