Rhiannon, a detective in the police force, wore a custom Alexis George gown, while Ferguson sported a black tux and bowtie.
The couple exchanged vows in front of family and friends at an intimate ceremony at Golding Wines in Lobethal.
Several of Ferguson’s South Australian teammates including Alex Carey, Travis Head, Tom Cooper, Chadd Sayers, Jake Weatherald and Jake Lehmann were in attendance.
Callum and Rhiannon met four and half years ago and were engaged for just over a year, before tying the knot.
The newlyweds will now enjoy a relaxing honeymoon in Mauritius as husband and wife before Ferguson returns to the cricket pitch with UK county cricket club Worcestershire next month.
It continues a season of romance with fellow South Australian star Megan Schutt marrying long-time partner Jess late last month.
Redbacks bowler Nick Winter and partner Laura celebrated their engagement on Christmas Day, while batsman Tom Cooper and wife Ebonie welcomed baby Violet Grace late last month after the pair were married in Byron Bay in July last year.