For very low relaxation time (i.e. lesser than a microsecond) viscoelastic fluid experimental determination is difficult, if not impossible. In the present work the relaxation time measurement of a weakly elastic polymer solution, too low to be measured using classical rheometry techniques, is assessed using a mixed experimental-numerical strategy. First the fluid is rheologically assessed, by measuring its shear viscosity, surface tension and density. Then the relaxation time is determined by comparing the jetting of polymer solution from a Continuous Ink-Jet (CIJ) device experimentally and numerically. The numerical approach is first validated using test case and a viscoelastic Oldroyd-B model is then used to model the experimental solution. The relaxation time is then a parameter allowing us to fit numerical simulation onto experimental results. This mixed strategy is particularly convenient for weakly elastic solution for which physical parameters can not be measured using experimental rheometry setup.