Yes, and it is a very common step as a business grows. Strictly speaking, Singapore does not offer a direct 'conversion' – a sole proprietorship and a private limited company are separate legal entities – so the process is to incorporate a new private limited company and transfer the business into it.
The usual steps are: incorporate the new company with ACRA; transfer the business's assets, and where appropriate its trade and goodwill, to the company (often documented by a sale or transfer agreement); novate or re-sign key contracts, leases, licences and supplier or customer arrangements in the company's name; move the business bank account, GST registration and employee arrangements across; and then cease the sole proprietorship with ACRA.
Incorporating brings important advantages – limited liability, a distinct legal identity, easier access to funding, and the 17% corporate tax rate with start-up and partial tax exemptions – but it also adds compliance obligations such as annual returns and statutory filings.
Apexia can manage the whole transition, from incorporating the company to transferring the business and closing the sole proprietorship, so nothing falls through the gaps.