  We present deep polarimetric observations of the European Large Area ISO
Survey-North 1 (ELAIS-N1) field using the Low Frequency Array (LOFAR) at
114.9-177.4 MHz. The ELAIS-N1 field is part of the LOFAR Two-metre Sky Survey
deep fields data release I. For six eight-hour observing epochs, we align the
polarization angles and stack the 20"-resolution Stokes $Q$, $U$-parameter data
cubes. This produces a 16 deg$^2$ image with 1$\sigma_{\rm QU}$ sensitivity of
26 $\mu$Jy/beam in the central area. In this paper, we demonstrate the
feasibility of the stacking technique, and we generate a catalog of polarized
sources in ELAIS-N1 and their associated Faraday rotation measures (RMs). While
in a single-epoch observation we detect three polarized sources, this number
increases by a factor of about three when we consider the stacked data, with a
total of ten sources. This yields a surface density of polarized sources of one
per 1.6 deg$^2$. The Stokes $I$ images of three of the ten detected polarized
sources have morphologies resembling those of FR I radio galaxies. This
represents a greater fraction of this type of source than previously found,
which suggests that more sensitive observations may help with their detection.
