At around 8.30am on Sunday 28th April, a member of the public reported finding vehicle tracks on land within the Easter Fodderlie estate.
When officers attended and carried out inquiries at the scene, they found two deer carcasses and two badger carcasses.
These animals have been taken for forensic examination and inquiries are ongoing.
Anyone with information is asked to come forward.
Wildlife Crime Co-ordinator, Constable Steven Irvine, said: "We are awaiting the findings of the forensic analysis, but believe at this time that the deer and badgers have been illegally poached and we are treating this matter very seriously.
"If you have any information that can help us find those responsible and bring them to justice, then please contact police immediately."
Those with information can contact Hawick Police Station via 101 and quote incident number 1186 of the 28th April. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.