In this Paper we report on phase resolved I –band optical spectroscopic and photometric observations of Cir X–1 obtained with the Very Large Telescope . The spectra are dominated by Paschen absorption lines at nearly all orbital phases except near phase zero ( coinciding with the X–ray dip ) when the absorption lines are filled–in by broad Paschen emission lines . The radial velocity curve of the absorption lines corresponds to an eccentric orbit ( e = 0.45 ) whose period and time of periastron passage are consistent with the period and phase predicted by the most recent X–ray dip ephemeris . We found that the I –band magnitude decreases from 17.6 to \sim 16.8 near phase 0.9–1.0 , this brightening coincides in phase with the X–ray dip . Even though it is likely that the absorption line spectrum is associated with the companion star of Cir X–1 , we can not exclude the possibility that the spectrum originates in the accretion disc . However , if the spectrum belongs to the companion star , it must be a supergiant of spectral type B5–A0 . If we assume that the compact object does not move through the companion star at periastron , the companion star mass is constrained to \hbox to 0.0 pt { $ < $ } { } _ { { } _ { { } _ { \textstyle \sim } } } 10 M _ { \odot } for a 1.4 M _ { \odot } neutron star , whereas the inclination has to be \hbox to 0.0 pt { $ > $ } { } _ { { } _ { { } _ { \textstyle \sim } } } 13.7 ^ { \circ } . Alternatively , the measured absorption lines and their radial velocity curve can be associated with the accretion disc surrounding a 1.4 M _ { \odot } neutron star and its motion around the centre of mass . An absorption line spectrum from an accretion disc is typically found when our line–of–sight passes through the accretion disc rim implying a high inclination . In this scenario the companion star mass is found to be \sim 0.4 M _ { \odot } . However , from radio observations it was found that the angle between the line–of–sight and the jet axis is smaller than 5 ^ { \circ } . This would mean that the jet ploughs through the accretion disc in this scenario , making this solution less probable .