The expression take as input is similar in concept to take as given, which has an entry of its own in the Merriam-Webster.
In the discussion of an algorithm, sometimes we want to focus on the general logic as opposed to the specifics of a particular calculation. We identify some things as constants (pi=3.1416), some things as rules to follow in the calculation, and other things as input. We can then talk about the properties of the algorithm, e.g. that perhaps its speed of execution goes up when the value of the input goes down.
To put this in a larger context: A fundamental model of computation is the Turing Machine, which has input, output, state and transition rules. The expression takes as input has become the conventional form because people have been talking and writing about computer algorithms for many decades now, and distinguishing between input and state is often an important part of the discussion.