You can definitely apply to any of the management consulting firms, as Eyad mentioned consulting firms do look for candidates with a diverse educational background.
I can use myself as an example, I have a background in biochemistry but managed to get job offers from a number of consulting firms before accepting a role with Accenture as a management consultant. I eventually moved to Ethos and Co (a boutique strategy firms founded by ex-Mckinsey managers) where I worked on strategy projects.
What is important as a student trying to enter your chosen industry is to understand what these companies are looking for in a candidate - As a management consultant is that there are 3 key skills that you need to demonstrate in your cover letter, CV & interviews.
Key skills to demonstrate in your CV/Cover letter:
1. Strong logical thinking and problem solving skills
Your job as a consultant is to help other businesses (your clients) solve their problems. This can be a number of things for example client`s sales are decreasing to new competitors entering the market to business expansion..etc. Client will expect you and your team to come up with a solution for them which should be structured and data driven
2. Good interpersonal & communication skills
Your job as a consultant will involve a lot of interactions with clients, your team and your bosses. It is important that you can get along well and build rapport with your clients so they can give you the data you need and to make you less stressed haha In addition to this, you need strong communication skills to present your solutions to your clients and your supervisor
3. A good team player
A typical day as a consultant involves you working with your consulting team in the clients office, team`s project will tend to be quite intense and you wont have much time to complete it hence it is important that you can work effectively in a team and be reliable
You need to look into your experiences so far and try to find examples that can demonstrate these skills, and my last advice, if you can connect with a consultant currently working in the company and they allow you to use their name in your applications. There will be a higher chance that HR will take notice and call you in for an interview : )
Good luck with your applications and definitely speak to some of our management consulting mentors that has helped mentees like you find our more about landing a job in management consulting