The interim leader was put in charge of the party following the resignation of Kezia Dugdale.
Anas Sarwar and Richard Leonard are currently contesting a leadership bid for the top role in the party.
The move comes after claims by his former partner that Mr Rowley sent abusive text messages.
In a statement, Mr Rowley said: “I totally refute these allegations and will take all steps necessary to clear my name.
“These allegations must be properly and thoroughly investigated in line with our party’s procedured - and I will refer myself to the party so such an investigation will take place.
“While that investigation is carried out, i wil lstep aside as deputy leader, as well as interim leader of the Scottish Labour Party.”