If your protein is at least somehow similar to a known protein with known active site, you have a chance to predict the active site residues. Otherwise it will be tough and is in my opinion not proper science. Otherwise structural biology would not be required anymore.
I would suggest to try to send the sequence to Phyre2 in order to make a model. This tool indicates also on which similar structure the models are based and how reliable the algorithm thinks the model is. Then you can look at the homologs and their active sites (if known), and check if these residues are conserved.
There are many algorithms that predict the active sites of proteins just from the aminoacid sequence. I think the one that are based on hydrophylicity of aminoacid sequence is the best first approach.