Yes you can get pregnant by use of a disposable syringe.
If you put sperm into a disposable syringe and insert the disposable syringe into your vagina or into the woman's vagina it is possible to get pregnant.
That is as long as you're fertile and can reproduce and as long as the sperm is fertile as well.
Some men have non fertile sperm and some woman are not fertile or have other issues causing them to not become pregnant.
So you may not always get pregnant even if you do insert sperm through use of a syringe but it can sometimes result in pregnancy.
Sometimes you may also require fertility treatments as well.
But if you're unable to get pregnant through regular sex then using a syringe with some fertile sperm can help you become pregnant.