There's a balance that needs to be struck between visibility and pervasiveness. Ideally, the clan would want a system that gets the attention of all players, ensuring that any interested to not miss it, but is not obtrusive (i.e., spam). The easiest way I can think of would be to have some sort of recruitment message appear during the two events that all players experience - joining and leaving the server. Both options have problems, though. Displaying the message at the beginning runs the risk of being overlooked as players instinctively tap '1' to close the rule menu. No matter how much we want them to, players will avoid reading the rules that have been set - must accept and work with that. Displaying the message at the end creates only logistical errors. Players who crash or leave prematurely wouldn't see the message. I'm not familiar with how much control steam provides admins, so I'm not sure if displaying it as they elect to leave is even viable.
Goals should be kept in mind while planning this. The point of this advertising would be to make players aware of their options, not to do our job for us. It can't be beat over their head, and it can't seem impassive or distant. Nothing irks me more than something addressed to me that looks like it didn't even care who I was. "Dear Sir and/or Madam". Ugh. What finally persuaded me to join this clan after a year or so of (on and off) playing was an individualized approach from a member. They were asking /me/ to join. Not asking if anybody wanted to. Me. I felt wanted, and, when entering a community, that's something that should be there. As a long-time member of a previous clan that (unfortunately) fell apart several years ago, I've had experience with what we called "clan-hoppers". Not sure if that term is still in use. Basically, they're players who hop from clan to clan. The type who seems like they're in a clan to be in a clan, not because they want to be with the people in the clan. I'm sure you've come across the sort at some point. Many experiences with these types of players have made me wary of players who ask to join as soon as a recruitment message appears, especially if I am unfamiliar with them.
Work has been keeping me away from game recently and I normally avoid reading the chat in-game. I don't know the real content of these messages, but your post made it sound like they were recruitment offers. I apologize if I misinterpreted.