This is from このすば{konosuba}, "GOOD'S BLESSING ON THIS WONDERFUL WORLD!", right?
First, From the viewpoint of grammar, I also guess this "と" is close to "とする". (I agree with Claire-san).
In this case, it is close to "~と書き記す" (note that), "と報告する" (report that) or "と判断する"(judge that).
For example,
"準備完了っと。" (I report/judge) complete preparation.
"これでよしっと。" (I report/judge) It's done. It's great.
"これで終わりっと。" (I report/judge) I'm finished.
Every "と" means "とする。" or "としよう。".
Even if we don't have to report this to someone, we sometimes or often use this.
I guess that most tasks or works are things someone tells/asks you to do.
(Not everyone does/addresses initiatively tasks/works.)
If you finished it, you may report that to someone.
Then, I think we might get to use this "と" even if we don't have to report.
Or, you just talk to yourself. "I talked to myself that I am finished."
We are not sure if which is correct, but you can guess it from the context.
In this case, Kazuma feels this is a task/work for him asked by someone. At least not initiatively/spontaneously.
Especially, Kazuma is a lazy and rude boy as you know.
He finished his task and doesn't have to report this to someone, but he feels he was forced to do this task.
So, I think he used this "と".
俺は適当に励ますと。
(She is bothering me, but I have to encourage her. I'm done though I am not so serious and faithful. so, I report) I said something encouraging.
I think the author of このすば wants to express that Kazuma is a lazy and rude person.
Or, perhaps, he might just talk to himself.
俺は適当に励ますと。
I said something encouraging. (And I talked to myself, "I'm done!")
Like he writes his diary.
In this case, I think the former(repot) is correct, but not completely sure.
If you met a similar situation like this, please guess it from the context.
Either way, this "と" in this sentence implies "not serious". He might feel even funny.
We don't use this "と" when we are serious.
Perhaps, the author of このすば! might want to express just "he is never serious" and not consider this "と" deeply.
By the way, please note the way to use "と" is almost same as "と" may have a rude nuance.
We rarely use this "と", but I sometimes see the way to use "と" like this in Manga or Anime.
For example, when you were told to finish your homework by your friend, you can say
"もう終わらせましたよ~と。"
This "と" might be too casual and a little bit acting silly.
You can show your sense of superiority or probably frustration/annoyance to his/her advice/scolding/lecture.
Anyway, it means, you feel a little bit against his/her advice or lecture, and you want to fan his/her feeling, worrying about you, angry or something.
We rarely use this because it is rude.
I don't remember that Kazuma uses this "と", but I think he also uses this... He is a rude boy as you know...