This doesn't seem quite right to me.

[Rileyk90]

I am trying to write out what i have going on during my school week in japanese everyday on my whiteboard to get extra practice. I have a sociology test tomorrow and I was wondering if someone would check this sentence. 明日、僕は社会学のテスト有る。 what I'm trying to say is "Tomorrow I have a sociology test."

[chikara]

There is a particle missing.

I believe ある is usually written in kana.

明日、僕は社会学のテストがある。

You could also use 受ける meaning "to take a test";

明日、僕は社会学のテストを受ける。

[Rileyk90]

Thanks! on my board I had written it with を following テスト. Would that work in the place of が ?

[TJack]

Thanks! on my board I had written it with を following テスト. Would that work in the place of が ?

No, because ある can't take a direct object, you can't "ある" something. ある just states that something (an inanimate object) exist.

[chikara]

Thanks! on my board I had written it with を following テスト. Would that work in the place of が ?

No, を marks the direct object of an action, ie the thing that is acted upon. ある, "to have", does not have an object but a subject, ie what do you have, so it uses the subject marker が. Having something, in this context, is a state rather than an action.

If you use 受ける, "to take a test", then you use を as the test is the direct object of the "taking", an action.

Edit: As per TJack-san's post it is probably better to think of ある as "exists" rather than "to have" which then makes it clearer that it is not an action.