Electroweak production of the top quark is measured for the first time in $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$, using a data set collected with the CMS detector at the LHC and corresponding to an integrated luminosity of $36\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. With an event selection optimized for $t$-channel production, two complementary analyses are performed. The first one exploits the special angular properties of the signal, together with background estimates from the data. The second approach uses a multivariate analysis technique to probe the compatibility with signal topology expected from electroweak top-quark production. The combined measurement of the cross section is $83.6\ifmmode\pm\else\textpm\fi{}29.8(\mathrm{stat}+\mathrm{syst})\ifmmode\pm\else\textpm\fi{}3.3(\mathrm{lumi})\text{ }\text{ }\mathrm{pb}$, consistent with the standard model expectation.