Yes you can. The general processing time is 4 working days.
If you want to apply for a Z visa, you are required to provide following materials:
a. Original and copy of Authorized Notification Form for Visa Application or invitation letter.
b. Both original and copy of Alien Employment License issued by the Ministry of Human Resources and Social Security, or Foreign Expert Work Permit issued by the State Administration of Foreign Experts Affairs of China.

c. Authorised Notification Form for Visa Application and documents proving family relations (e.g. marriage or birth certificate) for spouses and children of the applicants.

d. Original and copy of Physical Examination Record for Foreigners of those who will work in China for more than 6 months.

e. Z-Visa is valid for 3 months for a single entry with no specified duration of stay. One is obliged to apply for residence permit at the local public security bureau within a month after entering China.