"Round and round the garden" is an English language nursery rhyme typically accompanied by fingerplay.
It has a Roud Folk Song Index number of 19235.
The version given by The Oxford Dictionary of Nursery Rhymes is:[1] Round and round the garden Like a teddy bear; One step, two step, Tickle you under there!
[2] Since teddy bears did not come into vogue until the twentieth century it is likely to be fairly recent in its current form, but Iona and Peter Opie suggest that it is probably a version of an older rhyme, "Round about there":[2] Round about there Sat a little hare, The bow-wows came and chased him Right up there!
The adult reciting the verse starts by tracing an index finger in circles on the child's upturned palm, then walks their fingers up the arm with each "step", ending with a tickle under the child's arm.