In the current datasheet of STM32F103 (DocID13587 Rev 17) it is written:
5.3.14 NRST pin characteristics
The NRST pin input driver uses CMOS technology.
It is connected to a permanent pull-up resistor, RPU (see Table 35).
In few project we did, we noticed there is no internal pull-up on this pin. (and we needed to add an external pull-up to ensure the mcu work).