Unfortunately not as a typical memory card. Sony went with a proprietary memory card for the vita which makes them pretty expensive, even for small amounts of storage.

If you plan to play games digitally, you can go with the SD2Vita (like this one) and use a micro sd card with it for storage.

However, you would have to mod your vita and you would be using the game slot for the memory card, so you couldn't play physical games while it's in use. It is definitely the best option to have a large amount of storage at a fair price and avoid sony's overpriced cards.

If interested, hop on r/vitahacks!

Just get one from Amazon, that’s what I did. 30/10 would recommend this