  The $p_{\rm T}$-differential production cross sections of the prompt (B
feed-down subtracted) charmed mesons D$^0$, D$^+$, and D$^{*+}$ in the rapidity
range $|y|<0.5$, and for transverse momentum $1< p_{\rm T} <12$ GeV/$c$, were
measured in proton-proton collisions at $\sqrt{s} = 2.76$ TeV with the ALICE
detector at the Large Hadron Collider. The analysis exploited the hadronic
decays D$^0 \rightarrow $K$\pi$, D$^+ \rightarrow $K$\pi\pi$, D$^{*+}
\rightarrow $D$^0\pi$, and their charge conjugates, and was performed on a
$L_{\rm int} = 1.1$ nb$^{-1}$ event sample collected in 2011 with a
minimum-bias trigger. The total charm production cross section at $\sqrt{s} =
2.76$ TeV and at 7 TeV was evaluated by extrapolating to the full phase space
the $p_{\rm T}$-differential production cross sections at $\sqrt{s} = 2.76$ TeV
and our previous measurements at $\sqrt{s} = 7$ TeV. The results were compared
to existing measurements and to perturbative-QCD calculations. The fraction of
cdbar D mesons produced in a vector state was also determined.
