I started two weeks ago and it’s been absolutely terrible for me so far. It’s so difficult to make friends; by the time I moved in everyone had their own cliques. Even my roommate didn’t necessarily want to speak to me as she has her own high school friends that are attending the same college. So far, I’ve talked to some acquaintances but they all stop inviting me to lunch/dinner within the matter of a few days. I was so used to having people in high school to talk to and I assumed at college people just as or perhaps even more friendly. However, nobody invites me anywhere! I even sit alone during meals which I absolutely hate. All I really do is sit in my dorm all day and my roommate probably thinks I’m a loser because of it. I’ve tried to join clubs but it just makes me feel even more awkward. I’m three hours away from home and I talk to nearly nobody here. It stinks because it seems everyone has their own friends and are out going to parties and having a blast while I’m in my dorm crying alone. I thought college was supposed to be the best four years of your life. This is honestly the most miserable I’ve ever really felt in my life. 
Maybe you should try inviting some people instead of waiting for them to invite you.
Keep trying clubs, get a campus job, look for people to study with from your classes, look for a volunteer activity near campus. All of those are ways to meet more people. Keep busy, don’t mope in your dorm room.
The secret is everybody looks busy and happy but deep down inside everybody tries to fit in. Kid #1 learned this the hard way, after a few months, one girl broke down that the other two roommates were ignoring her. She was a daughter of a high level executive in Hollywood. Keep trying or not even trying. Be yourself, you will find friends.
Just try to put yourself in the middle of things. If you don’t want to sit alone, don’t; find a table even if it’s full and ask to pull up a chair and introduce yourself. Now, I admit that at my college most everyone is insanely friendly, so I’ve had no problems making friends even as an out of state student at a mostly commuter college, but try. Some of the cliques may not be as formed as you think. I’ve seen one that I’m sort of part of, but last week it barely existed and people were still getting to know each other, no one knew each other before the start of school.
Listen to the good advice here. You have been there for three weeks. Real relationships take a long time to cultivate and effort every single day to maintain.
I second the job. If you have time to sit in your room, you have 8-10 hours per week for a job at the library, the student union, working at the sports venue.
I think if someone is sitting alone at the cafeteria, others may assume you WANT to be alone - you are studying, or whatever. What albert69 said - just go to a table with other people, ask if you can sit with them - of course, they will say Yes! because most people are nice and friendly and open to meeting new people - then introduce yourself.
It may be hard the first time, but after that, it won’t be.
Also, don’t stay in your room - get out and go to a cafe and study, even if by yourself, go take a walk, go to a social event on campus… Go down to the lounge and see who’s hanging out there.
I third the job. People often meet new friends on the job.
Does your school have a Reddit forum? I see a lot of posts on Reddit forums where people say - hey I want to hang out and it always surprises me how many people respond that they are in the same boat. They arrange to meet somewhere like the dining hall or library.
You are not the only one who is having trouble. Lots of good suggestions here.
If you’re going to keep on focusing on the bad side you might not be able to turn things around. Be more active, maybe try to join some clubs or something? keep yourself from thinking it’s the worst place to be. Because whatever happens you have to look into different perspective of things because there are always better ways to look at them.
Maybe try an Xbox One? PS4? It would give people incentive to come and visit you.
Job, church activities, invite others to join you. Two of those three. The jobs on campus are likely to be posted on the college website. Apply for a few!