Hello Tobias Litherland (and thanks for the heads-up Xander Bakker):
If you have Pro installed, that's the easiest route -- it ships with SciPy, and is usable today. Further improvements are coming soon to our other products, but that doesn't help you for solving your immediate needs. For that, you can try using Python path files (.pth) to bridge between the environments.
WARNING: This approach is risky, and can potentially break your Python installation, so be careful, and this isn't a directly supported method. Because you're using different versions of packages like NumPy under the hood, strange things can happen, and sometimes introduce crashes.
1. Find the site packages path for your Anaconda install. On my machine, it was C:\Miniconda\envs\default\Lib\site-packages. Copy that path into a file called anaconda.pth.
2. Copy anaconda.pth into C:\Python27\ArcGIS10.3\Lib\site-packages (or the correct location if you used a different installation path).
3. Open Python, type:
import sys
print(sys.path)
If it worked correctly, you should see a new entry for the Anaconda environment from within the ArcGIS installed version of Python, and import scipy should work. Again, note that this may cause other problems, and if anything is breaking, delete the pth file to return your setup to a stock install.
Cheers,
Shaun