Short answer
Generally, yes -- but which type of business you can run depends on your citizenship and residence status. Any foreigner, regardless of residence status, can establish a capital company (sp. z o.o., simple joint-stock company, or joint-stock company). Running a sole proprietorship, general partnership, or professional partnership is more restricted.
What this depends on
EU/EEA citizens, US and Swiss citizens, and foreigners holding certain residence titles (permanent residence, EU long-term resident status, Blue Card, specific temporary residence permits for family reunification/study/research, refugee or subsidiary-protection status, temporary protection, or a valid Karta Polaka) can freely run a sole proprietorship. Foreigners outside these categories can still establish a capital company -- just not a sole proprietorship.
Documents / steps
- Decide which business form fits your status (capital company if you don't qualify for sole proprietorship)
- A capital company can be registered remotely, without needing to be physically present in Poland or hold a residence permit, if managed by proxy
- If you want to personally manage the company from within Poland, you'll need a legal residence title (a national D visa or a temporary residence permit)
Important exception
Owning a company does not, by itself, grant residence rights. It can be a basis for applying for a temporary residence permit for business activity, but that requires separately showing the business is real and financially viable.
Official source
Biznes.gov.pl -- official Polish business information portal, directly verified.
Related Auranik service
Business Setup in Poland can help review which structure fits your situation.