Yes of course. The sent circuit is a simple, but complete Li-Ion charger. The first step is to connect the power supply of 9-12V to the input. Adjust the output voltage to 4,2V (using the R4) without the battery. Connect the battery and that’s all. The circuits will cutoff the current when the voltage reaches the 4,2V. You can leave the battery connected to the charger. The charging current depends on the R1 resistor (Ich=UBE/R1 approaching =0,7/R1)
:!: Sorry, there was a print mistake on the previews schematics. I corrected them, so the recent one is good. (The mistakes was the next: the output voltage must be adjusted to 4,2V for one cell (one of BL-5C) and not 8,4V. The 8,4V is when you use two batteries in series. The output current is not 850mA, it refers to the capacity (850mAh). The output current is approaching 700mA using R1=1OHM)