Is it possible to install scipy under pypy?

Yes, it is possible, starting from Scipy 1.1.0. New enough PyPy (>= 6.0.0) and Numpy are however required, numpy>= 1.14.3, and preferably numpy>=1.15.0 when it's released. Installation can be done via the usual

pypy3 -mpip install numpy
pypy3 -mpip install scipy

assuming you have BLAS/LAPACK installed, so first you should make sure you are able to install numpy/scipy on normal Python from sources.

Nobody probably has tried whether this works with Pypy on Windows, so you are on your own there. It also probably won't work with NumPyPy --- you need the vanilla Numpy.

The other answers say "No" since that was the situation before May 2018.

Seems that the link in @piv.s great answer does not contain what is needed anymore. For installing BLAS/LAPACK and avoiding installation errors such as NotFoundError: no lapack/blas resources found on Ubuntu first run:

sudo apt-get install libatlas-base-dev

Then using the pip that corresponds to your pypy (not the system's):

pip install numpy
pip install scipy

or the one mentioned by piv. will do the trick.

No. SciPy has bits and pieces talking to cpython's C API, and pypy does not support that.

EDIT: As of May 2018, this is incorrect, and scipy is pypy-compatible. See the answer by @pv. for details.