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In this article, we take the $Y(4260/4220)$ as the vector tetraquark statewith $J^{PC}=1^{--}$, and construct the$C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$type diquark-antidiquark current to study its mass and pole residue with theQCD sum rules in details by taking into account the vacuum condensates up todimension 10 in a consistent way. The predicted mass$M_{Y}=4.24\pm0.10\,\rm{GeV}$ is in excellent agreement with experimental dataand supports assigning the $Y(4260/4220)$ to be the$C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$type vector tetraquark state, and disfavors assigning the $Z_c(4100)$ to be the$C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$type vector tetraquark state. It is the first time that the QCD sum rules havereproduced the mass of the $Y(4260/4220)$ as a vector tetraquark state.

Lowest vector tetraquark states: $Y(4260/4220)$ or $Z_c(4100)$