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 8-hour observing epochs, we align the polarization angles and stack the 20"-resolution Stokes Q, U-parameter data cubes. This produces a 16 deg2 image with 1QU sensitivity of 26 μJy beam-1 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 deg2. 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 sources than previously found, which suggests that more sensitive observations may help with their detection.