How to make mathematica give 1/0 as infinity

Use the two-arg version of ArcTan instead:

ArcTan[0, 4]

π/2

You can convert expressions of ComplexInfinity to Infinity by using the ReplaceAll operator /..

ArcTan[4/0 /. ComplexInfinity -> Infinity]

which gives Pi/2 as output.

On the off chance that what is desired in a computational environment in which n/0 evaluates to (positive) Infinity and t = ArcTan[..] falls in the range -Pi/2 <= t <= Pi/2. One should use caution when overwriting built-in functions. I doubt this will cause problems in computations in which n/0 should always mean positive Infinity and not ComplexInfinity.

ClearAll[evaluateWithRealPower];
SetAttributes[evaluateWithRealPower, HoldFirst];
evaluateWithRealPower[code_] :=
  Internal`InheritedBlock[{Power},
   Unprotect[Power];
   Power[0, p_?Negative] := Infinity;
   Power[0., p_?Negative] := Infinity; (* optional *)
   Protect[Power];
   code];

evaluateWithRealPower[ArcTan[4/0]]
(*  \[Pi]/2  *)