Parapsychology is “the field of study that deals with paranormal phenomena in psychology.” (OED). Paranormal is defined as “supposed psychical events and phenomena such as clairvoyance or telekinesis whose operation is outside the scope of the known laws of nature or of normal scientific understanding; of or relating to such phenomena.” (OED). Parapsychology studies phenomenon which are outside of the scope of normal scientific understanding. E.g., phenomenon which cannot be studied using the scientific method. Therefore, parapsychology is not a science.
Modern parapsychologists recognize that they are not scientists in the modern sense of the word, which is why they publish papers saying that the notion of science should be redefined. This redefinition is, of course, far more inclusive, less rigorous and generally more friendly to parapsychologists. Proper controls and repeatability, the former rarely being present, and the latter never having been present in parapsychology experiments, are not necessary.
To the extent that a parapsychologist follows the scientific method, and establishes a career that consists solely of publishing negative results, they may call themselves scientists. Judging by a scan through the Journal of Scientific Exploration, and others, this is not the state of the field, and most parapsychologists practice pseudo-science.
These comments are inspired by the bollocks in this thread.