  We obtained 128 high signal-to-noise ratio Stokes $V$ spectra of the B3V star
$\iota$~Her on 5 consecutive nights in 2012 with the ESPaDOnS
spectropolarimeter at the Canada-France-Hawaii Telescope, with the aim of
searching for the presence of weak and/or complex magnetic fields.
Least-Squares Deconvolution mean profiles were computed from individual
spectra, averaged over individual nights and over the entire run. No Zeeman
signatures are detected in any of the profiles. The longitudinal magnetic field
in the grand average profile was measured to be $-0.24 \pm 0.32 $ G, as
compared to $-0.22 \pm 0.32$ G in the null profile. Our observations therefore
provide no evidence for the presence of Zeeman signatures analogous to those
observed in the A0V star Vega by Lignieres et al. (2009). We interpret these
observations in three ways. First, we compare the LSD profiles with synthetic
Stokes $V$ profiles corresponding to organised (dipolar) magnetic fields, for
which we find an upper limit of about 8~G on the polar strength of any surface
dipole present. Secondly, we compare the grand average profile with
calculations corresponding to the random magnetic spot topologies of Kochukhov
& Sudnik (2013), inferring that spots, if present, of 2 degrees radius with
strengths of 2-4 G and a filling factor of 50% should have been detected in our
data. Finally, we compare the observations with synthetic $V$ profiles
corresponding to the surface magnetic maps of Vega (Petit et al. 2010) computed
for the spectral characteristics of $\iota$ Her. We conclude that while it is
unlikely we would have detected a magnetic field identical to Vega's, we would
have likely detected one with a peak strength of about 30 G, i.e. approximately
four times as strong as that of Vega.
