Ask other colleagues from your office how they view this. Maybe you would find that the ringing phone is a nuisance to everybody what then can give you all different position in bringing it forward.
Also, politely explain your problem to senior, ask him to turn the phone on silent because of frequently distracting ringtone. If your senior says the main reason of keeping the phone on sound alert is that he cannot hear vibrating well under some conditions and there is a risk that a call will be missed, there is a solution: bluetooth hands-free earpiece paired with that mobile phone. This way he will hear the phone on larger distance (typically up to 2 rooms away) without distracting everyone else. This can also accelerate productivity of the senior, because how can he/she currently work effectively with keyboard and mouse while on the phone without a handsfree (or does he/she currently use headphones for calls)?
Or this can be solved using a smart watch which indicate the phone ringing. It does not need to be the latest model, model like A1S sold for about $18 does the job perfectly. Your company should be able to afford that.
It is not the case that the senior has the right to set up everything based on their needs. Part of seniority is supporting the team in productivity, so true senior should address this concern and seek solution acceptable for everyone.
Also, if the ringtone should be a necessity, but it is too fancy (for example, a catchy melody), perhaps senior could at least change it to typical phone sound, which is less obtrusive. Hearing "We are the champions" 20 times a day (while always interrupted in different time of play) would not let me stay cool.
Also, if you have some official corporate values like teamwork or innovation, they can become your arguments should the senior resist the change. But it needs to be done wisely.
Even if the ringing is work-related, in today's era it is easy and cheap to overcome this problem and simple 'no' from senior is not a solution, seniority puts expectations on finding a solution for team. Consider going to your boss if there will be simple 'no' without any further effort shown.