The graviton is not part of the Standard Model, in the same way that gravity is not part of it. There are two reasons behind this.
- We don't have any theory of quantum gravity. There is a lot of research on this, but the answer is not there established.
- Gravity effects are negligible by tens of orders of magnitude at all energy scales currently probed. Therefore, they won't affect predictions for anything observable today.
For the second reason, the direct observation of a graviton is thus not something we could do today.
I hope this clarifies.