ACR FLT CREW ENCOUNTERS TURB WHILE CLBING TO ALT AND DEVS FROM ASSIGNED COURSE; CAUSING LOSS OF SEPARATION AND A TCASII RA.

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WE WERE ASSIGNED A 40 DEG HDG AND CLB TO 17000 FT. ATC ASKED US TO TURN L TO 40 DEG HDG. I EXPLAINED WE WERE ALREADY ON A 40 DEG HDG. ATC THEN TOLD US TO FLY DIRECT INTXN S. AT THAT MOMENT; WE ENTERED TOWERING CUMULUS AND ENCOUNTERED MODERATE TO HEAVY TURB. I WAS UNABLE TO SEE OR ENTER DIRECT INTO THE NAV COMPUTER DIRECT TO INTXN S; BECAUSE OF THE TURB. THEN WE RECEIVED A TA FOLLOWED BY AN RA. OUR FULL ATTN WAS NOW FOCUSED ON THIS. AS WE CAME ON TOP OF THE CLOUDS; I OBSERVED THE OTHER ACFT ABOUT 2 OR 3 MI S; PARALLEL AND OPPOSITE DIRECTION TO OUR COURSE. I THEN WAS ABLE TO ENTER DIRECT INTXN S. ATC INFORMED US THAT THERE WAS A LOSS OF SEPARATION AND THAT WE HAD TURNED INTO THE OTHER ACFT. I WAS IN DISBELIEF AS I NEVER SAW THE CAPT COME R OF COURSE. IF WE DID GO R OF COURSE; IT WAS CAUSED BY THE TURB. ALSO; THIS WHOLE SCENARIO TOOK PLACE IN ABOUT 1 30 SECOND TIMEFRAME. I AM DISPLEASED THAT THE ATC CTLR DID NOT GIVE US A HDG AND ALT HOLD CONSIDERING HE HAD TO SEE THIS CONFLICT UNFOLDING BEFORE HIM. ASKING AN ACFT TO PROCEED DIRECT TO A FIX REQUIRES SOME TIME TO SET UP THE NAV COMPUTER. A HDG WOULD HAVE BEEN MUCH FASTER AND EASIER TO ACCOMPLISH IN HEAVY TURB.