  We present the results of precision timing observations of the binary
millisecond pulsar PSR J1640+2224. Combining the pulse arrival time
measurements made with the Effelsberg 100-m radio telescope and the Arecibo
305-m radio telescope, we have extended the existing timing model of the pulsar
to search for a presence of the effect of a general-relativistic Shapiro delay
in the data. At the currently attainable precision level, the observed
amplitude of the effect constrains the companion mass to
$m_2=0.15^{+0.08}_{-0.05} M_\sun$, which is consistent with the estimates
obtained from optical observations of the white dwarf companion and with the
mass range predicted by theories of binary evolution. The measured shape of the
Shapiro delay curve restricts the range of possible orbital inclinations of the
PSR J1640+2224 system to $78^{\circ}\le i\le 88^{\circ}$. The pulsar offers
excellent prospects to significantly tighten these constraints in the near
future.
