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 $78^{circ}le ile 88^{circ}$. The pulsar offers excellent prospects to significantly tighten these constraints in the near future.
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