A theme makes your website more friendly and attractive and to move your current theme from Magento 1 to 2 is impossible. Still, you can choose among the following different ways:

1. Find a free theme for Magento 2 and install it on the new store (included customization if needed) this will save your time and also money
2. Another alternative is to buy a quality ready-made theme for Magento 2 and install it on your store (included customization if needed) it is not only cheap but fast too.
3. Clone the old Magento 1 website to build a similar one for Magento 2 website (Magento 1 PSD design is required) but be ready to spend some extra money as it is expensive and it will take a lot of Time.
4. Clone your favorite website design to create a similar one for your store again this will cost you and time-consuming
5. Create a unique design from the scratch though you are doing everything from scratch so it will be an expensive affair and you have to dedicate a lot of time to it.

For a proper method, you need to determine your requirements, budget and time. Still, we would recommend you to go for the select option which is applying a ready-to-use Magento 2 theme. A number of Well-design Magento 2 themes and templates are available in the Market and you will get at affordable prices. If you use those themes then you just have to spend 1 week to install it on the new site and make some minor customization (only if you want) on the other hand, the third, fourth and fifth options are likely to take 1 month to conduct which will obviously increase the overall cost.