There is a hard (but better) way, and a very quick way that came out pretty good (image below):
1. The hard way is to use the Pen Tool to carefully create a selection of the signature. This is very time consuming and requires knowledge of the Pen tool, but you'll get the best results.
2. A quick way is to use the Magic Wand and select the red color (be sure to un-check the 'contiguous' setting). With that selection active, go to Select>Modify>Expand. I expanded by two pixels, which nicely captured the green stroke around the red lettering. If you're working on a larger version of the image you may need a different pixel setting. Copy that expanded selection to its own layer and convert the layer to a Smart Object. That will help you to scale it up without distorting too badly.