Rovers played with only one man up front throughout the match and never really showed the ambition required to make the breakthrough despite a number of near misses.
Swansea played some pretty football but were really no better and the outcome was one long yawn for the fans.
Both sides had severe injury problems but Doncaster were the worst effected with no less then seven men on the sidelines.
Swansea had the edge at the start playing some flowing football but they never really threatened the Rovers goal in the opening period.
But when Doncaster did manage to apply some pressure, Dean Shiels was cynically brought down by Angel Rangel after almost racing clean through in the eighth minute.
The resulting free-kick by Martin Woods was on target but visiting keeper Dorus de Vries punched the ball to safety.
On-loan striker Billy Sharp produced good movement in attack for Rovers but he endured a frustrating time as the home side's play was far too intricate when he was really looking for an early pass.
Doncaster enjoyed a spell of good fortune when Swansea went close three times in quick succession midway through the half.
Gorka Pintado just failed to convert from close range in the 23rd minute and then Thomas Butler's stooping header hit the bar following a corner seconds later.
Neil Sullivan saved at point-blank range from Craig Beattie in the 25th minute as Swansea battled to break the deadlock.
But they seldom threatened for the rest of the match and it was Rovers who went closest to scoring when John Spicer dribbled through straight from the restart only to fire inches wide.
Woods hit a left-foot shot just wide in the 69th minute and James Hayter fired wildly off the mark after de Vries had fumbled a free-kick as both sides had to accept the stalemate.