You can distill by taking the precaution of providing the top of your distillation column with a desiccant such as: P2O5 or Mg SO4

You can follow this article for drying Ethanolamine

Cu2O thin films were obtained from CuO films at drying temperatures lower than 290 °C and times shorter than 10 min in open atmosphere. A rapid transformation of CuO films to Cu2O films at 260 °C evidenced the existence of a useful reduction mechanism that was studied. A metal precursor solution was prepared from the mixing of copper acetate and monoethanolamine in isopropanol. Thin films of 5 layers were deposited by the dip-coating method at a withdrawal speed of 6 cm/min. Each layer was dried in a furnace at 230, 260, 275 or 290 °C for 5, 7 or 10 min. X-ray diffraction, reflectance and transmittance in the UV–Vis region and, specular reflectance in the infrared showed that CuO films are obtained at 230 °C. However, Cu2O with good crystallinity and transparency is produced with drying at 260 °C and above, for 10 min and less.

I doubt you need strictly anhydrous conditions. Using reagent grade ethanolamine should do it. Anyway ...

To remove some traces of water you coud store it o.n. over activated 3A-molsieve.

If you want bone dry ethanolamine, it is crucial to keep it under dry argon or nitrogen as it is hygroscopic. Therefor MgSO4 will fail.

Safia Taleb : Never use reactive acidic P2O5 with basic compounds like amines. It will not only fail, it is also higly DANGEROUS!!!

To dry alcohols, I prefer to reflux over magnesium, then distill off the dry compound from the magnesium alcoholate. Should work with ethanolamine as well, but you need to perform a vacuum distillation under inert conditions.

good luck

Thanks all for the answers. I will try a vacuum destilation with a 4A-molsieve at the colector flask. My professor recommend me this proceadure

Thanks Sebastián, for your remarks