The answer is no. The R&A and USGA rules defines a ball-marker as:
“An artificial object when used to mark the spot of your ball to be lifted, such as a tee, a coin, an object made to be a ball-marker or another small piece of equipment.
No mention of needing to be a round shape. However, in a recent PuttBANDIT survey of 1,200 UK golfers, we asked what type of ball marker they used to mark their golf ball on the green. At least 69% of the 1,200 responders were using a round marker.
What if the object used to mark the ball has a line on it? Equipment rule 6.7 – Definition of Alignment Device and Treatment of Ball-Markers (Rule 4.3) sets maximum size limits and dimensions on golf ball markers and their features (including lines) so they conform to rules and are not considered to be alignment aids. This limits golf ball markers to 2 inches horizontally and 1 inch vertically. The PuttBANDIT golf ball marker has been examined by the R&A and ruled to conform to the rules of golf.
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