According to "the Adoption History Project" the answer is to whether it was permitted is "yes":
Every state in the country currently allows single adults to adopt children. This may be less surprising than the fact that singles have been legally eligible to adopt since the first adoption laws were passed in the mid-nineteenth century. Indeed, the “spinster” who took in children was a staple of Victorian moral fiction and a recurrent figure in adoption narratives. A fair number of unmarried women (Jessie Taft was one) adopted children in the early decades of the twentieth century. They often raised children in pairs as well as alone, illustrating that the vast majority of adoptions by lesbians and gay men have been arranged as single parent adoptions, whether they actually were or not. But formal legal eligibility did not imply tolerance, let alone acceptance. Singles were viewed as less desirable parents than married couples. Men were considered far less desirable than women, if they were considered at all.
From what I read on that site, it seems single male adopters were frowned upon by society in general, but the literary examples of Little Orphan Annie and Batman and Robin show, it could be situationly approved of. But it seems in general, we don't really know how often it actually happened:
Still, single parents did adopt prior to the 1960s, although there is no way of knowing how many. The number was probably small. We know very little about who these adopters were or what kind of children they took in, although it is certain that most were women and probable that they adopted more relatives (i.e., nieces and nephews) than unrelated children. Adoption statistics offer few clues.