Turns out the sound is a bit more complex than one tone shifting upward. I located the .WAV file in the game's assets and examined it in Audition. Here's what it found:
(Focus on the bottom half. The y-axis represents frequencies, with 1k at just above the middle. The yellow and red colors show which frequencies are being used at different points on the x-axis, which represents time)
As you can see, there is indeed a build-up, but there are lots of tones involved even from the start. What this means is that it will probably be pretty difficult for someone who isn't experienced with audio programs to replicate from scratch.
That said, you can try to find pre-made sounds that are fairly similar. Here are a few examples I found after a brief search (note: I didn't check the licenses for these listings):
Simply searching "Sci-Fi" will give you tons of results just like these on FreeSound.org. I highly encourage you to find some sounds you like, then open them up in Audacity to do some tweaks like reversing them, slowing them down/speeding them up, etc. With the right sounds and a little tweaking, you can get pretty close to what you want with minimal work.
Oh, and pay attention to the license information for each track you use, and always give attribution when requested (and, heck, even when it isn't requested, it's still a nice thing to do).