Like anyone else, someone that is self employed can get a mortgage. They will need to have been self employed for a while, and typically this means being able to show 2-years financials for a bank. If you cannot yet show 2-years financials then a non-bank may still be an option.
As a mortgage adviser that specialises in helping self employed people I know that you may earn more than the financials show and know what expenses can be included back as income. Too often the banks do not include all of the income for self employed and that is a reason that so many self employed struggle to get a mortgage.