Yes, there are many algorithms that solve
cryptarithms, all of them implemented by computer
programs called "solvers".
In the Web you find four major online solvers:
 Truman Collinsīs "Alphametic Puzzle
Solver"
 Jorge Soaresīs "Alphametic Puzzle
Solver"
 IREAD.IT Alphametic Solver

Robert
Israel's "The Alphametic Applet"
Solvers #1 and #2 tackle additions only, whereas solvers #3 and #4 solve 5 types of
arithmetic operations: addition, subtraction, multiplication, division and exponentiation.
Fortunately, for solving a puzzle by hand there is not
such an universal algorithm. There are only some hints,
rules, strategies, etc., and oneīs sheer basic knowledge
of arithmetic and logical reasoning. This human and
challenging process of solving cryptarithms by hand is
just what gives us zest, exhilaration and that final
enjoyment when we "crack the code" getting the
solution.
