Yes, a material can be as a function of cathode or anode by just looking at cyclic voltammetry. If your test material operate in a -ve voltage window (below 0) then it means that your materials is anode and vice versa. Recently, I've done some experiments and confirmed this phenomenon from my own experience.
Muhammad Sajjad thank you for your comment. In a CV we can observe both +ve an -ve voltages being applied to the test material with a scan rate, at such cases how can we determine the property of the material?
Can I ask more about your goals with this project? You can in principle get almost any conductive material to act as either a cathode or an anode based on the potential you apply to that material, so long as you have a counter electrode to facilitate the closure of the circuit. The question is how good of an anode or cathode your material is, and that will largely depend on what reaction you want to occur within that material or at its surface.
To give a concrete example - and sorry here if I am using a different sign convention (these things can be tricky, but I come from a U.S. Chemical Engineering background): if I apply a cathodic (negative/reductive) potential to a platinum electrode in a conductive aqueous solution, I'll drive a net cathodic/reductive reaction (such as hydrogen evolution). If I apply an anodic (positive/oxidative) potential to that same platinum electrode in that same aqueous solution, I'll drive a net anodic/oxidative reaction (such as oxygen evolution). And if I have two platinum electrodes in the system at the same time, then one can act as a counter to the other; one will drive hydrogen evolution, and the other, oxygen evolution. There is nothing different about the electrodes or the solutions they are in, except the fact that I am controlling the relative potentials of the electrodes through the input of energy into a potentiostat (or similar device). Note: this is an electrolytic example, but I'm happy to discuss things from a galvanic cell perspective if that is more useful.
For example, you are using any COF based materials for CV and you don not know the potential window of the test sample. The better way is to look other's COFs based realted literature and run the CV as any COF potenial window like (-0.2-0.6, -0.4-0.4 etc). From this type of changing pitential window at the end you will at the proper and suitable window for your test material. Regarding to the potentails, you will see the related literature similar to the test sample or related to that materials family such as COFs as i discussed above. At end, you will explain the unknown details about the material. I hope it will helpful ...
Beside the electrode material, it is the electrolyte which determine the stability regarding the overall potential window. For example, the carbon based materials are usually stable in both positive and negative potential window. Then electrolyte pH (if using aqueous electrolyte) play an important role deciding the stability of potential window.