Before we get on to The Rules implications of playing with a broken club, it should be noted that, yes, you may well be able, technically, to play with a broken club. If the clubhead has come completely away from the shaft, you might struggle a little, but if the damage is relatively minor you would probably still be able to hit shots. Whether those shots are any good would depend on the severity of the damage (and your ability as a golfer of course.)
Anyway, that’s the practicality dealt with. This really is a Rules question on whether you are allowed to play with a broken club under The Rules of Golf. Well, the answer to the question is, maybe.
Rule 4.1a deals with clubs allowed in making a stroke and the key thing is that in making a stroke, a player must use a club that conforms to the requirements in the Equipment Rules. Those requirements are far too long to outline here, but there are requirements with regards the shaft, the head, the grip, the face, the length, the straightness… All sorts of things have to meet the requirements for the club to be conforming.
The important thing here is that to be conforming the club most meet those Rules requirements when either new or if the playing characteristics have been changed in any way. One of the ways those playing characteristics might have been changed is, if the club is broken. If you’ve broken any part of your club and it still adheres to the requirements in the Equipment Rules, you can use it.
If you break your club in competition, whether it’s accidental or through abuse, you can continue to use it for the remainder of that round, even if it has become non-conforming. But you can’t use it again after the round if it has become non-conforming, even in a playoff if you’re in a stroke play competition.
If the playing characteristics of a club have changed through normal wear, it is still conforming. So, if you have a scratch on the base of your driver or a small chunk out of the sole of your sand wedge, it is deemed to be still a conforming club.
But you must be quite careful. If for instance you accidentally bent the shaft or your putter more than five inches above the head. It would have become non-conforming, even if you were still comfortable using it. If you were to play a shot in your next competitive round using that putter, you would have broken Rule 4.1 and you would be disqualified. Remember you could still use it for the remainder of the round in which it became bent.
It is the players responsibility to ensure that his or her clubs conform to the Equipment Rules. Those equipment rules say that if the player has any doubt as to the conformity of a club, they need to ask The R&A or USGA. That’s quite a task. But thankfully for us lowly amateurs, queries may also be directed to the local committee in charge of a competition or the local Rules Committee. So, if you break your club but still want to use it, it’s worth checking with your committee before you use it again in competition.
Basically, the answer to the question of can you play with a broken club is, yes, but only if it still conforms to the requirements in the Equipment Rules.
