Can C-like function call syntax be easily achieved for particular function names?

There is a handy package, Notation, built-in to Mathematica. With it, we can do the following:

Needs["Notation`"]

Notation[ParsedBoxWrapper[RowBox[{"sqrt", RowBox[{"(", "x_", ")"}]}]]
         ⟹
         ParsedBoxWrapper[SqrtBox["x_"]]]

Notation[ParsedBoxWrapper[RowBox[{"sqr",  RowBox[{"(", "x_", ")"}]}]]
         ⟹
         ParsedBoxWrapper[SuperscriptBox["x_", "2"]]]

In the Mathematica Notebook interface, it looks like this (after Needs["Notation`"] has been executed, and then you selected the Notation[...] and pressed Ctrl+Shift+N):

After entering this code, we can simply do

d = sqrt(sqr(a)+2*a*R)

and get our output

Sqrt[a^2 + 2 a R]

Maybe you can use the fact that TraditionalForm by default interprets parentheses as function calls:

fromCString[s_String] := ReplaceAll[
    ToExpression[s, TraditionalForm, Defer],
    {
        sqrt -> Sqrt,
        sqr -> square
    }
]

Then:

fromCString["sqrt(sqr(x)+y*z)"]

Sqrt[square[x] + y z]