It appears from his writings and lectures that he was generally familiar with the most basic theoretical positions and debates in classical political economy -- the labor theory of value, the invisible hand, the theory of land rent, and the simple theory of a competitive market. And beginning with the marginal revolution (Jevons, Pareto, and Marshall), he seems to have studied economic theory more carefully. But I don't find any evidence in his corpus of a careful reading of Smith, Ricardo, or Malthus. So what was the source of his knowledge of classical political economy?
One source of exposure to the history of economics occurred during his first two years of teaching as a lecturer at Princeton. Tom Pogge indicates in John Rawls: His Life and Theory of Justice that Rawls did significant reading and study of political economy during 1950-52:
In the fall of 1950, he attended a seminar of the economist William Baumol, which focused mainly on J. R. Hicks's Value and Capital and Paul Samuelson's Foundations of Economic Analysis. These discussions were continued in the following spring in an unofficial study group. Rawls also studied Leon Walras's Elements of Pure Economics and John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior. (16)So there is some direct evidence of Rawls's reading in economics. Another way in which he might have gained a speaking acquaintance of the history of economics is through secondary surveys of the field. Were there standard histories of political economy in Rawls's formative years from 1950 to 1965?
One of the great historians of economic thought during those years was Joseph Schumpeter. Schumpeter's Ten Great Economists appeared in 1952. This book focuses largely on post-classical political economy; after a long chapter on Marx, Schumpeter provides short discussions of Walras, Menger, Marshall, Pareto, von Bohm-Bawerk, Taussig, Fisher, Mitchell, and Keynes. More important than TGE is Schumpeter's major contribution to the history of economic thought, History of Economic Analysis, which appeared posthumously in 1954. It is possible that Rawls used these books as a sort of intellectual guide to his understanding of the history of economic thought. The only reference to Schumpeter in Rawls's corpus is a single citation of Capitalism, Socialism, and Democracy in A Theory of Justice. This doesn't preclude the possibility that he read Schumpeter's histories of economics. But is there any basis for supposing that Rawls was in fact acquainted with Schumpeter's work?
Here is a clue worth pursuing. Pogge notes that Rawls spent a final year of fellowship at Princeton in 1949-50, and that he spent part of this time in an economics seminar with Jacob Viner, a distinguished Princeton economics professor. (The other main area of study during that year was in the history of U.S. political thought with Alpheus Mason.) And this establishes a tenuous connection to Schumpeter and the history of economic thought. Viner was a significant contributor to economic theory and policy in the 1930s and 40s at the University of Chicago and Princeton, and he also had a sustained interest in the history of economic thought. In 1954 he wrote one of the first (and most prominent) reviews of History of Economic Analysis in American Economic Review (link).
So here is a hypothesis: it seems likely enough that part of the work that Rawls did in 1949-50 with Viner was concerned with the history of economic thought, and it seems likely as well that he would have learned of Schumpeter's ambitious research on the history of economics from Viner. Schumpeter's book existed only in extensive notes and drafts at the time of his death in 1950 and was edited for publication by his wife, Elizabeth Boody Schumpeter, following his death. Exposure to Schumpeter through Viner would have given Rawls the motivation to study History of Economic Analysis carefully when it appeared in 1954. Rawls was an assistant professor of philosophy at Cornell by that time, and Pogge emphasizes his discipline when it came to reading and reflecting on the materials that he found relevant to his philosophical work.
Two other books on the history of economic thought that appeared during the approximate time period are Mark Blaug's Economic Theory in Retrospect (1962) and George Stigler's Essays in the History of Economics (1965). There are two references to Blaug in A Theory of Justice, so Rawls was certainly familiar with this book. Maurice Dobb's Theories of Value and Distribution since Adam Smith: Ideology and Economic Theory (1973) appeared a few years later.