Try setting `TextPadding -> True`.  It does more or less the same as the builtin  [`ContentPadding`](http://reference.wolfram.com/language/ref/ContentPadding.html).  It is described in SciDrawGuide.pdf.

Example:

    << SciDraw`

    labelFun[x_, _] := 
      Module[{frac = Rationalize[x/Pi] Pi, num, den},
        num = Numerator[frac];
        den = Denominator[frac];
        If[den == 1,
          num,
          StringForm["``/``", num, den]
        ]
      ]

    Figure[
     FigurePanel[{FigGraphics[
         Plot[Cos[\[Omega]t]^2, {\[Omega]t, -0.3, 2 \[Pi] + 0.3}]];}, 
      XPlotRange -> {-0.3, 2 \[Pi] + 0.3}, 
      XTicks -> 
       LinTicks[-2 Pi, 2 Pi, Pi/2, 4, TickLabelFunction -> labelFun],
      TextPadding -> True
      ],
     CanvasSize -> {5, 3}]

I'm not sure what the best way is to get correct spacing around the `/` sign, but the following works:  replace the string in `StringForm` with `"\!\(TraditionalForm\```/``\)"`.  This is a string representation of boxes.  I obtained it by writing a single character into a string, selecting it, then pressing Command-Shift-T to convert it to TraditionalForm.  This created a traditional form environment within the string. Then I deleted the character and typed what I wanted instead.

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/rHFlj.png