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:

1. Jorge Soares´s "Alphametic Puzzle Solver"
2. Naoyuki Tamura´s "Cryptarithmetic Puzzle Solver"
   

3. Truman Collins´s "Alphametic Puzzle Solver"
    
4. Robert Israel's "The Alphametic Applet"

Solvers #1, #2 and #3 tackle additions only, whereas solver #4 solves 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 one´s 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.