Is this move clearly losing for white? Chessgames.com shows 1 win and 2 losses for white only, and I could not find any other reference for this move.
[FEN ""] 1. e4 c5 2. Nf3 d6 3. a3?
No, it is not clearly losing, but I would say that the question mark is appropriate. You have to understand that white, by the nature of going first, can afford to waste a move in many early opening positions without it being a losing move. What it does though is it usually throws away any chance at gaining an advantage, and that is because you cannot be sure that the wasted move, in this case 3.a3?, will be helpful to your position as the position develops. In general, in the opening, you want to play moves that you KNOW will help you and that you know you want to play...you cannot know that about a3. a3 also does nothing to fight for the center. At best, you might play an early b4 trying to get play in the Wing Gambit.
In the Mega Database, there are actually 35 games, but the average rating for white and black is only 1796 to 1768, so that should tell you a lot: Strong players do not think it is good, even if not losing. For the record, white only scores a 37.1% with 3.a3?, but again, anything can happen between 1700s.
It's pretty bad but not close to losing. 3.a3 has been chosen in 34 games in my database, and scores around 38%. Stockfish at depth 28 gives an evaluation of about 0.14. So objectively speaking the game is equal after 3.a3 and White can't seriously hope for an advantage. It's also not one of those openings which you might play to trick your opponent, since pushing the a-pawn isn't threatening.
Other posters have shared database and Stockfish results, but I would prefer just to talk strategy. What, exactly, is your plan with 3. a3 ?
If you want to play b2-b4, you can already do that on move 3; it's called the Wing Gambit, and though it does not have a sterling reputation, you'll find masters who have won games with it, and can study those games.
Why do those masters who have played the Wing Gambit not play a3 first? Generally it's because a3 is a do-nothing move. Even if you get to play b4, black doesn't have to trade there, and if he doesn't, then you've given him a free move to execute his strategy.
What, then, is black's strategy? To fight for the dark squares in the center, specifically d4. The move a3 doesn't do anything to hinder that strategy.
So with those points in mind, I think Black has several good moves here. First, you have all of the normal Sicilian moves, like 3...Nc6, 3...e6, 3...a6, or 3...Qc7. Preparing a fianchetto of either bishop, 3...b6 or 3...g6, seems fine. But also you might be giving Black a chance to fight for d4 more directly with 3...e5!?. If Black has so many viable moves, it doesn't seem like you've gained anything over a normal Sicilian.
It's not a good move because it wastes a tempo and doesn't really accomplish anything.
However, it's not a horrible move because white still has a tiny advantage due to his better center and his lead in development (at least for now). Theoretically white could argue that since d5 is the equalizing move for black in the sicilian and black has "lost" a move playing d6 that white could possibly gain that tempo back. However, a3 doesn't give white anything at all so gaining the tempo back is one giant moot point.
Maybe there's an advantage in playing a waiting move and waiting for Nc6 before Bb5 but there should be several waiting moves that at least accomplish something.
Typically, the Sicilian is a battle between white's dynamic advantages and black's long-term advantages. If white plays slowly, black should be able to equalize fairly easily and take control of the initiative. That's probably the biggest reason something like this isn't played at high levels. Aside from that though there are several moves that accomplish everything a3 does but do other things as well.