Absolutely. What you're seeing is entirely normal in babies, particularly around 3+ months old. Among other things, he might be beginning to teethe; both of those things are associated with teething. Drooling is associated with basically everything for many babies, and sucking on fingers (or thumbs or other things) is also very normal.
If the drooling is truly excessive, you may want to talk to your pediatrician to ensure it's not due to a few particular causes (low muscle tone, in particular). Otherwise, buy a lot of bibs, and put a bib on him at all times, over his shirt, or under it if over is a problem. Make sure it's a safe bib (that cannot choke him). Many bibs must be removed for sleeping, although I think some are safe(r).