Angie
Your Rat will undoubtedly cause you problems, not least when he or she starts to breed prolifically, so leaving well alone is not an option. No doubt you are aware of the potential disease risk re Weils Disease etc, so the sooner it's gone the better.
If you can get close enough to poke it and annoy it then I would poke it and annoy it with the flat side of a spade, until it is itself flat !!
You can get rat poison to put down - place it inside some old drainage pipe or similar as this tends to keep the birds away from it - but most poisons are based on the drug Warfarin which thins the blood, and many rats today have developed a fair amount of immunity to it.
Me - I'd get an air rifle (or a friend with one) and plug it.- or borrow a terrier from someone and let it have a go! If you are into blood sports, a brush handle with barbed wire wrapped round the last foot makes a good Rat tickling stick.
And before everyone starts on about how cruel I am, I've worked on farms for years and have seen more rats than most and the damage and injury to stock they cause is unbelievable

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Rat

British by birth
Scottish by the Grace of God

Blog updated Wednesday November 13th