We carried out a millimeter wavelength line survey between 79 and 356 GHz with the IRAM-30m telescope to investigate the physical and chemical properties of the molecular envelope of the oxygen-rich AGB star IK Tau. We analysed the molecular lines detected using the population diagram technique to derive rotational temperatures and column densities. Additionally, we conducted a radiative transfer analysis of the SO$_2$ lines detected. For the first time in this source we detected rotational lines in the ground vibrational state of HCO$^+$, NS, NO, and H$_2$CO, as well as several isotopologues of molecules previously identified. We also detected several rotational lines in vibrationally excited states of SiS and SiO isotopologues, and rotational lines of H$_2$O ($\nu_{\mathrm{2}}$=2). We have also increased the number of rotational lines detected of molecules that were previously identified, enabling a detailed study of the molecular abundances and excitation temperatures. IK Tau displays a rich chemistry for an oxygen-rich circumstellar envelope. We highlight the detection of NS and H$_2$CO with fractional abundances of f(NS)$\sim$10$^{-8}$ and f(H$_2$CO)$\sim$[10$^{-7}$--10$^{-8}$]. Most of the molecules display rotational temperatures between 15 and 40 K. NaCl and SiS isotopologues display rotational temperatures higher than the average (~65 K). In the case of SO$_2$ a warm component with $T_{\mathrm{rot}}$$\sim$290 K is also detected. This SO$_2$ warm component is probably arising from the inner regions of the envelope (at $\sim$8$R_{*}$) where SO$_2$ has a fractional abundance of f(SO$_2$)$\sim$10$^{-6}$. This result should be considered for future investigation of the main formation channels of this, and other, parent species in the inner winds of O-rich AGB stars, which at present are not well reproduced by current chemistry models.< Réduire