Suisham previously kicked for Dallas in 2005 and 2006. He was released by Washington on Dec. 8 after missing a key kick -- the same problem that cost Folk his job Monday.
"I can't thank the Cowboys enough for giving me an opportunity with them," Suisham told ESPN.com's Matt Mosley. "I'm so happy and excited about it and I feel like I have a lot to offer the organization."
Folk clanged the right upright on an easy 24-yarder that would have put away Saturday night's 24-17 victory against the unbeaten Saints. Instead, the Dallas defense had to make one more stand against one of the league's best offenses.
Folk leads the NFL with 10 misses, going 18-of-28 and missing seven of his past 11.
Suisham was released by the Redskins in great part after he missed a short field goal against New Orleans, which rallied to win in overtime.
Suisham was one of five kickers the Cowboys brought to their facility for a workout Monday. The others were Shane Andrus, Parker Douglass, Steven Hauschka and Connor Hughes. Folk did not participate in the workout.
Suisham told Mosley he received a call from the Cowboys on Sunday but he wasn't able to get a flight out of northern Virginia because of all the snow. He woke up at 3 a.m. Monday and went to the airport to catch a flight that connected through Atlanta.
"It's been a long time since I've been on the tryout circuit," Suisham said to Mosley. "I sort of got used to those charter flights, so it was interesting to be back in the middle seat."
For his career, Suisham is 85-of-107 (79.4 percent). He originally signed with Pittsburgh out of Bowling Green in 2005, went to the Cowboys' practice squad and was signed to the active roster on Oct. 24. Suisham played in three games and was 3-of-4 on field goals before being released.
Back with Dallas in 2006, he played in three games and was 1-for-2 before again being cut. He finished the year with the Redskins, appearing in five games and converting 8-of-9 field goals. Suisham played in 16 games for the Redskins in 2007 (29-of-35) and 2008 (26-of-36) and 12 games in 2009.
Dallas tried several remedies while Folk piled up a six-game streak of at least one miss.
First, the Cowboys switched holders, replacing Mat McBriar with Tony Romo even though their quarterback is haunted by a critical flub late in a playoff loss at Seattle three years ago. Then they tried an in-house competition with kickoff specialist David Buehler, who proved unreliable on field goals.
Concerns eased when Folk nailed a 44-yarder just before halftime against the Saints, but it didn't take them long to come back.
"It's a mystery to us," Phillips said before Folk was cut. "We have tried to work it out a lot of different ways. Now it's come to this point."
Adding to the mystery, Folk had missed just 10 kicks in his 2½-year career before slumping. Television footage during Saturday night's game showed Folk's pregame kicks flying all over the place in the controlled atmosphere of the Superdome.
ESPN's NFL Insider Adam Schefter, ESPN.com's John Clayton, ESPNDallas.com's Tim MacMahon and The Associated Press contributed to this report.