You can allow your protein to fold again by removing your denaturant (e.g. in a chromotography column) but I think that you can't have the assurance of getting it back to its natural form, the refolding could create new structures.
i think it depends to the protein that was denatured, although most of the proteins are are not reform after denaturation as in the case of hemoglobin.
Many proteins may not refold successfully just by removal of the denaturant. Proteins that fold as preproteins or zymogens may not refold properly after proteolytic maturation. Even those that will refold may only do so under particular conditions, such as high dilution to avoid aggregation, the presence of certain substances (such as arginine or noncovalently bound cofactors), or the use of chaperones. In some cases, it may be necessary to reform the correct disulfide bonds by including a redox buffer.
In theory it is possible but experimentally problematic in most cases. The main issue is to find the best condition to favor the renaturation rather than aggregation.
Many companies sell refolding kits which allow for quick screening of refolding conditions, often in 96 well format. The question is whether you have a functional assay to assess whether your protein has refolded to its native state. Protein solubility is not always the best (functionally-relevant) readout.