请问stm32f105rc 64pin能通过串口烧写吗？

 这个应该是你的操作有问题，说说你的操作。

Flash_Loader_Demonstrator--这个软件是ST开发的专门用于串口下载程序的软件，可以识别HEX BIN文件，还是挺好用的。
    使用这个软件的前提，调试好串口电路，板载串口电路或者为开发板增加一个 USB转串口电路模块

 楼上正解、、、

应该是可以的，弄个max232就好

注意 BOOT 1，BOOT 0 两位
好像是一个接地，一个接3.3V吧
自己查查，很久不用，我不太记得了

肯定可以啊，电路要配合好

用STM32F105RB UART1 ISP 可以下载  另外:  
If USART1 is used to connect to the bootloader: the USART2_RX (PD6),
CAN2_RX (PB5), OTG_FS_DM (PA11) and OTG_FS_DP (PA12) pins have to be
kept at a high or low level and must not be left floating during the detection phase
悬空这些引脚也是可以下载的。没有问题

1） stm32都可以通过默认的串口1烧写（必须是默认的串口），这是因为stm32内置的固件只支持默认串口1.
2）串口需要max232等串口电路下载；
3）如不能下载，请检查uart电路是不是连接在默认串口1上，检查串口电路是否正常通讯

不能支持！
Bootloader unavailability on STM32F105xx/STM32F107xx devices
with a date code below 937
Description
The bootloader cannot be used if the USART1_RX (PA10), USART2_RX (PD6, remapped),
CAN2_Rx (PB5, remapped), OTG_FS_DM (PA11), and/or OTG_FS_DP (PA12) pin(s) are
held low or left floating during the bootloader activation phase.
The bootloader cannot be connected through CAN2 (remapped), DFU (OTG FS in Device
mode), USART1 or USART2 (remapped).
On 64-pin packages, the USART2_RX signal remapped PD6 pin is not available and it is
internally grounded. In this case, the bootloader cannot be used at all.
Workaround
• For 64-pin packages
None. The bootloader cannot be used.
• For 100-pin packages
Depending on the used peripheral, the pins for the unused peripherals have to be kept
at a high level during the bootloader activation phase as described below:
– If USART1 is used to connect to the bootloader, PD6 and PB5 have to be kept at a
high level.
– If USART2 is used to connect to the bootloader, PA10, PB5, PA11 and PA12 have
to be kept at a high level.
– If CAN2 is used to connect to the bootloader, PA10, PD6, PA11 and PA12 have to
be kept at a high level.
– If DFU is used to connect to the bootloader, PA10, PB5 and PD6 have to be kept
at a high level.

参考文件《AN2606  Application note  STM32 microcontroller system memory boot mode》

应该是可以的，弄个max232就好

肯定可以

可以的。与103是一样的