  We present findings of the detection of Magnesium II (Mg II, {\lambda} =
2796, 2803 {\AA}) absorbers from the early data release of the Dark Energy
Spectroscopic Instrument (DESI). DESI is projected to obtain spectroscopy of
approximately 3 million quasars (QSOs), of which over 99% are anticipated to be
at redshifts greater than z > 0.3, such that DESI would be able to observe an
associated or intervening Mg II absorber illuminated by the background QSO. We
have developed an autonomous supplementary spectral pipeline that detects these
systems through an initial line-fitting process and then confirms the line
properties using a Markov Chain Monte Carlo sampler. Based upon a visual
inspection of the resulting systems, we estimate that this sample has a purity
greater than 99%. We have also investigated the completeness of our sample in
regard to both the signal-to-noise properties of the input spectra and the
rest-frame equivalent width (W0) of the absorber systems. From a parent catalog
containing 83,207 quasars, we detect a total of 23,921 Mg II absorption systems
following a series of quality cuts. Extrapolating from this occurrence rate of
28.8% implies a catalog at the completion of the five-year DESI survey that
will contain over eight hundred thousand Mg II absorbers. The cataloging of
these systems will enable significant further research because they carry
information regarding circumgalactic medium environments, the distribution of
intervening galaxies, and the growth of metallicity across the redshift range
0.3 < z < 2.5.
