Answer: Economists lean right because they understand economics.
Assuming that “right wing” means an ideological position that favors free enterprise, private property and individual rights, then it is easy to see why economists are generally right-wingers.
It has been accurately said that there is only one economic system, and that is one of voluntary exchange in free markets (free markets don’t have barriers to entry or exit) in which prices guide the supply and demand of goods and services. Economists are people who understand how this complex order emerges from the activities of individuals and groups. Many of the conclusions students of economics reach are counter-intuitive; they appear to be against common sense. It is fair to say that if one is not trained in economics, one is likely to reach wrong conclusions about how and why the extended order of the market — the Great Society, in the words of Hayek — operates.
So at one end of the spectrum there’s the economic system. It depends on freedom and voluntary action, which is the essence of cooperation. At the other end of the spectrum is the political system, where the primary instrument is coercion, not voluntary cooperation. Force is used to make people bend to the will of others. These others can be a democratic majority or a dictator or an autocrat. In a political system, some person (or a collective) other than the individual (or a voluntary association of individuals) determines what people may do.
Socialism, communism, etc., are not alternative economic systems. There is only one economic system; the collectivist systems are political systems.