In a very broad sense, yes it can. We have some very important proteins in our bodies called tumour suppressors which act to stop cell growth and division when things have gone wrong in order to prevent cancer. In a lot of cancers, these DNA encoding these proteins is damaged so the proteins are no longer produced or are not acting the way they are supposed to. Therefore, the cell is not protected against damage and will keep growing rapidly- which is how cancer is formed.
On the other side, we have oncogenes which promote cancer. These are often proteins involved in speeding up cell growth and division. If you have to much of these proteins, then you can develop cancer.
Sometimes you will need less tumour suppressors and more oncogenes to cause cancer- it’s all about the balance of both. There are many oncogenes and many tumour suppressors- so often the cell can pick up these problems and remove the damaged cells before any cancer occurs. Unfortunately, this isn’t always the case.
I’m sure others might be able to add some more explanation as there’s so much that could be said! I just don’t want to give you a really long boring answer. If you want more detail, feel free to ask!
As Loren said, depending on the protein, having too much or it, or not enough can be enough to cause cancer.
Sometimes it is a combination of having too much of one thing and not enough of some others which can cause people to get cancer.
Cancer isn’t the only disease which works like this either, lots of diseases are caused by a change in one protein either causing it not to act like it normally does or changing the amount of it in a cell.
As the others said, cancer is a complicated, but important, subject to study. There are many scientists and bioinformaticians who are looking at which genes are switched on or switched off in patients with different cancers. The switching on or off of these genes results in having too much or too little of some proteins. As Loren and Lucy said, it can also be when the protein is made incorrectly.
We are studying some proteins, called Fc gamma receptors, which live on the surface of cells. In a normal human, these cells help remove infection from cells and so can start the process of killing tumor cells. But in lots of cancers, these proteins stop working properly and so the tumor is not killed. So in this case it is the protein so working properly.