To follow with Ra2 which is a deadly attacking move.
Anderssen's Opening

It's basically a waiting move. It gives Black the opportunity to decide the opening, which White will respond to accordingly. It's very transpositional and flexible.
Its main weakness is that it pretty much negates White's first move advantage, especially if 1. a3 turns out to be a waste of time later on in the game. It also lets Black do whatever he wants with his first move.

For instance, it is useful if u play against a scotch specialist.
Indeed, 1.e4 e5 2.Nf3 Nc6 2.d4 exd4 3.Nxd4 Qh4?! is interesting but doubtful, white's best reply being Nc3 followed by Ndb5 or Ndb5 straight away. But with a3 here, u control b4...
1.a3 can be useful in some reversed Queen's gambit accepted, because u could consider taking on c5, then b4, a3 holding these pawns...
Or playing some Chebanenko slav tempo up, not a great deal but if u like some of these variations with black, why not...

1.a3 d5 2.c4 dxc4 3.Nf3 Be6 4.Ng5 Bd7 5.e4 e5 6.Nf3 Be6 7.Qc2 b5 8.d3 cxd3 9.Bxd3 a6 10.a4 b4 11.Ng5 Nf6 12.Nxe6 fxe6

1... d5 is definitely the best answer. 1... e5 is met by 2. e4 and Black is unable to play ... Bb4, so he has to play the Reversed Italian or the Reversed Scotch.

@chesster : i wonder if u read me about the scotch...
On 1.a3, 1...g6 (or even better 1...Nf6 followed by g6) is supposed to be best, because thats the move where a3 is less useful.
Anyway, to understand all the subtleties on 1.a3, white has to know many variations, because of the transpositions...
So playing 1.a3 just because : "to avoid theory", would be a huge mistake.
What are the main strategical plans for this opening i.e. 1.a3?