Yes. It is possible to turn energy into matter.
This is what Physicists believed happened at the start of the Universe in the Big Bang.
Initially there was an enormous amount of energy and as time went by (I mean by this is the
first few fractions of a second of existence) this energy turned into matter. The fundamental
particles were formed first and these then joined together to make atoms which themselves
joined together to form molecules and finally into the matter that we recognise I the world
around us today.
Physicists can recreate this situation in the so-called Pair
Production. This is where a gamma ray photon ("pure energy"), above certain energy, can
become a positron and electron – hence the name pair production. This occurs in the
intense fields that exist close to the nucleus of an atom, in a way the gamma ray makes a
collision with the nucleus.
The trouble with all the preceding explanations is that
matter and energy are interchangeable. The gamma ray photon above does indeed have a
"mass" and the electron and positron does have a "rest energy". It really is a question of what
we are observing at a particular moment.