In ANSI C (meaning C89 or C90), you do not have to declare a function prototype; however, it is a best practice to use them. The only reason the standard allows you to not use them is for backward compatibility with very old code.
If you do not have a prototype, and you call a function, the compiler will infer a prototype from the parameters you pass to the function. If you declare the function later in the same compilation unit, you'll get a compile error if the function's signature is different from what the compiler guessed.
Worse, if the function is in another compilation unit, there's no way to get a compilation error, since without a a prototype there's no way to check. In that case, if the compiler gets it wrong, you could get undefined behavior if the function call pushes different types on the stack than the function expects.
Convention is to always declare a prototype in a header file that has the same name as the source file containing the function.
In C99 or C11, standard C requires a function declaration in scope before you call any function. Many compilers do not enforce this restriction in practice unless you force them to do so.