You don’t add the gauge to your finished product. Rather, you do it beforehand to see what dimensions your knitted stitches and rows have. Gauge is a method of quantifying your tension, which, ideally, should match the tension indicated in the pattern, so that the fabric you produce will match the one intended by the pattern.
But all of this is kind of moot, because you’re knitting a scarf. Gauge is important when it comes to fitted items, sweaters and the like. When it comes to a scarf, you have a lot more leeway.
If you like, you can knit a gauge swatch, (but it probably isn’t necessary for this project). Cast-on 20 or so stitches and just knit and purl back and forth to create a stockinette sample. Then measure how many of your stitches add up to four inches. If it’s 14 stitches, then you’re right in line with what the pattern calls for.
The vertical gauge for this pattern is 18 rows, but really, vertical gauge is pretty irrelevant when it comes to scarf making, since all it determines is length. Just keep knitting till the scarf is as long as you want it, then bind-off. Done!
My advice would be to ignore the specified gauge, and just experiment with the yarn a little. Using those needles and the way you knit, does the fabric come out the way you want it to? Or is it too tight (in which case you can use a larger needle) or too loose (try a smaller needle)?
Once you find a tension you like, cast-on for the project and knit away. It’s a scarf, so “fit” doesn’t really matter, just the suppleness of the fabric.